Consider the following statements :
Statement 1 : The function `f:IRtoIR` such that `f(x)=x^(3)" for all "x""inIR` is one-one.
Statement 2 : `f(a)impliesf(b)" for all "a,binIR` if the function f is one-one.
Which one of the following is correct in respect of the above statements ?

Options

A. Both the statements are true and Statement 2 is the correct explanation of Statement 1.
B. Both the statements are true and Statement 2 is not the correct explanation of Statement 1.
C. Statement 1 is true but Statement 2 is false.
D. Statement 1 is false but Statement 2 is true.

Answer

A

Explanation

`f(x)=x^(3)`
`f(x_(1))=x_(1)^(3)`
`f(x_(2))=x_(2)^(3)`
if `x_(1)=x_(2)`
then `f(x_1)=f(x_(2))`
So it is one-one function
Hence option (a) is correct.