Question

If the real-valued function $f\left(x\right)=px+\sin x$ is a bijective function, then the set of all possible values of $pϵR$ is?

• A. $R-\left\{0\right\}$
• B. $R$
• C. $(0,\infty )$
• D. None of these

Answer 1

The correct option is A $R-\left\{0\right\}$

Given, the function $f\left(x\right)=px+\sin x$ is a bijective function. Which implies, there exists a function $g\left(x\right)$ such that $f\left(g\right(x\left)\right)=g\left(f\right(x\left)\right)=x$ for, $xϵR$.

This argument doesn't work if $p=0$ because it would involve division by zero.

Hence, the set of all possible values of $pϵR$ is $R-\left\{0\right\}$.