If the function (f: R \rightarrow R) is defined by (f(x)=|x|... | Mathematics | SolveeIt | Solveeit

Today, August 18

Question

If the function $f: R \rightarrow R$ is defined by $f(x)=|x|(x-\sin x)$ , then which of the following statements is TRUE?

A

$f$ is one-one, but NOT onto

B

$f$ is onto, but NOT one-one

C

$f$ is BOTH one-one and onto

D

$f$ is NEITHER one-one NOR onto

Answer

$f$ is BOTH one-one and onto

Explanation

Solution

The Correct Option is (C): $f$ is BOTH one-one and onto