Question

Let $f$ and $g$ be two functions on $R$, defined as $f\left(x\right)=x^3+4$ and $g\left(x\right)=\sqrt[3]{3x-4}.$ Then $\left(gof\right)\left(x\right)$ is

• A. $\sqrt{x^3+4}$
• B. $x$
• C. $\sqrt{x^3-4}$
• D. $(x^3+4)\sqrt[3]{3x-4}$

Answer 1

The correct option is B $x$

We can infer from the given functions that, $f$ and $g$ are inverse of each other.
$\therefore \left(fog\right)\left(x\right)=\left(gof\right)\left(x\right)=x\forall x\in R$