Determine the domain and range of the relation R defined by R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}

(i) f(x) = –|x|, x ∈ R  We know that  || = { , ≥ 0;   −, < 0  ∴ () = −|| = { −, ≥ 0 ; , < 0  Since f(x)...

R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}  ∴ R = {(0, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}  ∴ Domain of...

R = {(a, b): a, b ∈ Z, a – b is an integer} It is known that the difference between any two integers is always an integer.  ∴ Domain of...

A = {9, 10, 11, 12, 13} f: A → N is defined as f(n) = The highest prime factor of n  Prime factor of 9 = 3  Prime factors of 10...

The given real function is f (x) = |x – 1|.  It is clear that |x – 1| is defined for all real numbers.  ∴ Domain of f = R Also, for...

The given real function is () = √( − 1) It can be seen that √( − 1) is defined for  ≥ 1.  The given function is  Therefore, the domain of...

R = {(x, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}  ∴ R = {(0, 5), (1, 6), (2, 7), (3, 8), (4, 9), (5, 10)}  ∴ Domain of...

The relation R from A to A is given as R = {(x, y): 3x – y = 0, where x, y ∈ A} i.e., R = {(x, y): 3x =...

R = {(a, b): a, b ∈ Z, a – b is an integer} It is known that the difference between any two integers is always an integer. ∴ Domain of R...

The given real function is f (x) = |x – 1|. It is clear that |x – 1| is defined for all real numbers. ∴ Domain of f = R Also, for x...