Question

If the real-valued function $f\left(x\right)=px+\sin x$ is a bijective function then the set of possible values of $p\in R$ is

• A. $R-\left\{0\right\}$
• B. $R$
• C. $(0,+\infty )$
• D. $|p|>1$

Answer 1

Answer: (D)

$|p|>1$

$f\left(x\right)=px+\sin x$
$f^{\prime }\left(x\right)=p+\cos x$
For given function to be bijective,
$f^{\prime }\left(x\right)>0\forall x\in R\Rightarrow |p|>1$