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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 ?

Mathematics 2015 NDA Mathematics 2015 NDA 2015

Options

Both the statements are true and Statement 2 is the correct explanation of Statement 1.

Both the statements are true and Statement 2 is not the correct explanation of Statement 1.

Statement 1 is true but Statement 2 is false.

Statement 1 is false but Statement 2 is true.