Bissoy.com
Doctors Medicines MCQs Q&A

A real-valued function f satisfies the relation f(x)f(y) = f(2xy + 3) + 3f(x + y) - 3f(y) + 6y, for all real numbers x and y, then what will be the value of f(8)? 

A real-valued function f satisfies the relation f(x)f(y) = f(2xy + 3) + 3f(x + y) - 3f(y) + 6y, for all real numbers x and y, then what will be the value of f(8)?  Correct Answer 19

Calculation:

f(x) f(y) = f(2xy + 3) + 3f(x + y) - 3f(y) + 6y

∴ Putting x = y = 0,

⇒ f(0) f(0) = f(2 × 0 × 0 + 3) + 3f(0 + 0) - 3f(0) + (6 × 0)

⇒ f(0)2= f(3) + 3f(0) - 3f(0) + 0

⇒ f(3) = f(0)2

Putting y = 0,

⇒ f (x) f (0) = f (2 × x × 0 + 3) + 3f (x + 0) - 3f (0) + (6 × 0)

⇒ f (x) f (0) = f (3) + 3f (x) - 3f (0)

⇒ f (x) f (0) = f(0)2 + 3f (x) - 3f (0)

⇒ f (x) f (0) - f (0)2= 3f (x) - 3f (0)

⇒ f (0) * (f (x)- f (0)) = 3 * (f (x)- f (0))

∴ Either f(x) = f(0) or f(0) = 3

Since, all functions can’t have the same value, f(0) = 3

∴ Putting x = 0, y = 3,

⇒ f (0) f (3) = f (2 × 0 × 3 + 3) + 3f (0 + 3) - 3f (3) + (6 × 3)

⇒ f(0) f(3) = f(3) + 3f(3) - 3f(3) +18 = f(3) +18

⇒ 3 f(3) = f(3) + 18

⇒ f(3) = 9

∴ Putting x = 0, y = 8

⇒ f (0) f (8) = f (2 × 0 × 8 + 3) + 3f (0 + 8) - 3f (8) + (6 × 8)

⇒ 3f(8) = f(3) + 3f(8) – 3f(8) + 48

⇒ 3f(8) = 9 + 48.

⇒ f(8) = 19

∴ The value of f(8) is 19.

Related Questions

Let Z be the set of real integers and R the set of real numbers. The sampling process may be viewed as partitioning the x-y plane into a grid, with the central coordinates of each grid being from the Cartesian product Z2, that is a set of all ordered pairs (zi, zj), with zi and zj being integers from Z. Then, f(x, y) is a digital image if (x, y) are integers from Z2 and f is a function that assigns a gray-level value (that is, a real number from the set R) to each distinct coordinate pair (x, y). What happens to the digital image if the gray levels also are integers?
Study the following information carefully and answer the question given below. The following criteria have been introduced for the appointment of a scientist in a research organization. Candidates: 1) Must be a postgraduate in Mathematics/Physics/Chemistry subject with a minimum of 65% marks 2) Age should not be less than 26 years and not more than 35 years as on 01-01-2018 3) Must have a post-doctoral degree with more than 50% marks 4) Should have a minimum of 3 years of experience in the above fields 5) Should be prepared to be under probation for one year If the candidate satisfies all the criteria other than (3), he may be designated as Project Scientist. If the candidate satisfies all the above criteria other than (3) and (4) he may be referred for the post of Junior Scientist. If the candidate fulfills all the above criteria with 7 years of experience in the relevant fields, he/she can be designated as a Senior Scientist. If the candidate fulfills all the above criteria with 12 years of experience in the relevant field, he/she can be designated as Principal Scientist. Varun's age is 27 years as of 1/1/18, he obtained his bachelor's and master's degree in chemistry with 72% and 76% marks respectively. He also had 4 years of experience in the relevant field and was ready to be under probation for one year of the job. to what position he may be assigned
Read the passage carefully and select the best answer to each question out of the given four alternatives.
Public opinion may be passive and false or active and real. It is claimed in theory that all governments are ultimately based on the opinion or sanction of the governed. But we find that in practice the people's rights are often trodden down and tyranny and oppression are allowed to continue. The government does it not because the people want it to do so but because they are too idle, too uneducated and too disunited or timid to oppose the govern ment. Such public opinion is passive and false and not an active verdict. But when we find people alert, intelligent and determined to let the government know their will, when they want to exercise actively their voice in the management of their country, we have an instance of true or active public opinion. True public opinion is formed by and expressed through the press, the platform, political parties and educational institutions. These have sacred duties to perform, duties on which depends the ultimate good of the entire community. The press today wields a tremendous influence, So it should support the causes and move ments and condemn the wrong one's and thus teach people to form correct opinion. A free and fair press ventilates the grievances of the public. Thus a healthy relationship develops between the people and the government through out an unbiased press. Political parties also help to create and regulate opinions. No less important part is played by the educational Institutions which train the minds of the young people who will be the citizens of tomorrow. It has been said that modern Germany and China have been made by their universities. It is necessary that the young and the growing minds should imbibe the spirit of fellow-feeling, the spirit of tolerance, the habit of compromise, and show due regard for the feelings and opinion of others without which a democratic society cannot function, let alone succeed. When there is true awakening of the people, we shall have the real and conscious public opinion. And justice will reign on earth and truly will the voice of the people be the voice of God.
What is important for the democratic society to function properly?
Consider with respect to HusserI's concept of phenomena.
1. Phenomena is a substantial unity that has real properties, real parts and real changes.
2. Phenomena is no substantial unity, that has no real parts and no real changes.
3. Phenomena has no nature, but only essence.
4. Phenomena have no essence, but only nature.
The following are the criteria set by a Retail outlet for the selection of candidates for the post of Store In charge in a reputed mall. 1. The candidate must be a graduate in any stream with minimum of 50% marks. 2. The candidate must have Minimum of 5 years of Sales experience in Retail. 3. The age of the candidate should not be less than 25 years and more than 34 years as on 1st October, 2019. (a) If a candidate satisfies all the criteria except 2 as given above but has an MBA degree and has minimum of 2 years of work experience in sales, she/he must be sent to the General Manager, Recruitment for further interview. (b) If a candidate satisfies all the criteria except 3, but has more than 5 years experience as a Group Manager and above in Sales managing a team of sales executives, then she/he must be sent to the Regional Manager, Sales & Marketing, for further interview Based on the above criteria and conditions, analyze and decide which of the following course of action should be taken for the candidate whose description is provided below. Please note that you are not to assume anything other than the given information. Sujoy is a graduate with 55% marks and MBA through Correspondence. He was born on Sept 20, 1990. He has 1 year of work experience as a sales executive and 2 years of experience as a Group Manager, Sales. On the basis of the information as given above, which of the following decisions would be appropriate
The following are the conditions for selecting list of a suitable candidates to be called for interview after the written test for the recruitment is conducted/ organized for management-level persons of a multi-national company. For providing accounting services and sales the candidates must (a) be holding a graduation in basic science with 65% or above or B. E degree with 55% and above marks (b) have passed the written test with 70% or above marks (c) the age must be in the group 25 to 30 years as on 1/4/18 (d) have experience in an accounting firms for three years and diploma in accounting with 60% or above marks (e) be presently drawing CTC of 6 Lakhs per annum and above In case the applicant who satisfies all other terms above except 1) at (a) above, then be referred as Junior Accountant 2) at (d) & (e) above then be referred as Trainee-Accountant Satisfying all the above with experience of 5 years then be referred as senior-Accountant Satisfying all the above criteria (a-e) with CA/ ICWA / MBA (Finance) then be refereed as manager (Accounts) Read all the above information and answer the following question Shravani has passed H. SC with 72% of marks. She has done diploma in accountancy with 62% of marks. She was working with an organization in the field of accounting in the field of accounting from 4 years and was drawing CTC of 6.5 Lakhs presently. She is 28yrs as on July 2018. She may referred for the position of:
According to Naiya̅yikas we ascertain the relation of universal concomitance between x and y :  (A) We can determine the relation only if we can determine the relation of essential identity between x and y   (B) By perceiving that in all cases the presence of x is accompanied by the presence of y  (C) We can determine the relation only if we can determine the relation of cause and effect between x and y  (D) By not perceiving any instance where the presence of x is not accompanied by the presence of y or vice-versa.  Choose the correct answer from the options given below : 
The following are the conditions for selecting list of a suitable candidates to be called for interview after the written test for the recruitment is conducted/organized for management - level persons for a multi - national company. For providing accounting services and sales the candidate must (a) be holding a graduation in basic science with 65% or above or B.E. degree with 55% and above marks (b) have passed the written test with 70% or above marks (c) the age must be in the group 25 to 30 years as on 1/4/18 (d) have experience in an accounting firms for three years and diploma in accounting with 60% or above marks (e)  be presently drawing CTC of 6 Lakhs per annum and above In case the applicant who satisfies all other terms above except 1) at (a) above, then be referred as Junior Accountant 2) at (d) & (e) above then be referred as Trainee - Accountant Satisfying all the above with experience of 5 years then the referred as senior-Accountant Satisfying all the above criteria (a - e) with CA/ICWA/MBA (Finance) then be referred as manager (Accounts) Read all the above information and answer the following question Praveen has done his Masters in physics. He has no experience in accounting neither diploma. He is ready to be on training for accounting after joining. For which position he may be referred
The following are the conditions for selecting list of a suitable candidates to be called for interview after the written test for the recruitment is conducted/ organized for management-level persons of a multi-national company. For providing accounting services and sales the candidate must (a) be holding a graduation in basic science with 65% or above or B.E degree with 55% and above marks (b) have passed the written test with 70% or above marks (c) the age must be in the group 25 to 30 yrs as on 1/4/18 (d) have experience in an accounting firms for three yrs and diploma in accounting with 60% or above marks (e) be presently drawing CTC of 6 Lakhs per annum and above In case the applicant who satisfies all other terms above except 1) at (a) above, then be referred as Junior Accountant 2) at (d) & (e) above then be referred as Trainee-Accountant Satisfying all the above with experience of 5 yrs then be referred as senior-Accountant Satisfying all the above criteria (a-e) with CA/ ICWA/ MBA (Finance) then be refereed as manager (Accounts) Read all the above information and answer the following question: Radha Mohan has done her graduation in physics with 58% of marks. She has passed the written examination with 76% of marks. She is 27 yrs as on June 2018. She has the experience in the accounting company for four years with salary of 7 Lakhs per annum. She also has passed diploma in accounting with 61% of marks. She may be referred for the position of:
The following are the conditions for selecting a list of suitable candidates to be called for interview after the written test for the recruitment is conducted/ organized for management-level persons for a multi-national company. For providing accounting services and sales the candidate must (a) beholding graduation in basic science with 65% or above or B.E. degree with 55% and above marks (b) have passed the written test with 70% or above marks (c) the age must be in the group 25 to 30 years as on 1/4/18 (d) have experience in an accounting firm for three years and a diploma in accounting with 60% or above marks e) be presently drawing CTC 6 lakhs per annum and above In case the applicant who satisfies all other terms above except 1) at (a) above, then be referred to as Junior Accountant 2) at (d) & (e) above then be referred to as Trainee-Accountant Satisfying all the above with experience of 5 years then be referred to as senior-Accountant Satisfying all the above criteria (a-e) with CA/ICWA/MBA (Finance) then be referred to as manager (Accounts) Read all the above information and answer the following question   Praveen has done his Masters in physics. He has no experience in accounting neither diploma. He is ready to be on training for accounting after joining. For which position he may be referred.