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Consider the following statements: Statement 1: The function f : R → R such that f(x) = x3 for all x ∈ R is one-one Statement 2: f(a) = f(b) ⇒ a = b for all a, b ∈ R if the function f is one-one. Which one of the following is correct in respect of the above statements?

Consider the following statements: Statement 1: The function f : R → R such that f(x) = x3 for all x ∈ R is one-one Statement 2: f(a) = f(b) ⇒ a = b for all a, b ∈ R if the function f is one-one. Which one of the following is correct in respect of the above statements? Correct Answer Both the statements are true and Statement 2 is the correct explanation of Statement 1.

Concept:

One-to-One functions define that each element of one set say Set (A) is mapped with a unique element of another set, say, Set (B).

if f(x) = f(y) implies x = y, then f is one-to-one

Calculation:

1. f(x) = x3

f(x1) = x13 and

f(x2) = x23

f(x1) = f(x2) ⇒ x13 = x23

This is one-one function

This statement is correct.

2. f(a) = f(b) ⇒ a = b

Which is definition of one-one function.

Hence, option (1) is correct.

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