Question

Let the function $f:R\to R$ be defined by $f\left(x\right)=2x+\sin x,x\in R$. Then, $f$ is

• A. One-one and onto
• B. One-one but not onto
• C. Onto but not one-one
• D. Neither one-one nor onto

Answer 1

The correct option is A One-one and onto

$f:R\to R$ be defined by $f\left(x\right)=2x+\sin x$

$f^{\prime }\left(x\right)=2+\cos x$

Since $-1\le \cos x\le 1$, $f\left(x\right)=2+\cos x>0$

So, $f\left(x\right)$ is strictly monotonic increasing.

Hence, $f\left(x\right)$ is one-to-one and onto