Question

Verify that the two given functions are inverses of each other

f(x)=x3+1andg(x)=√3 x−1

Answer 1

$f(x)=x^3+1$

Domain: $(-\infin, \infin)$

Range: $(-\infin, \infin)$

$$f(g(x))=(\sqrt[3]{x-1})^3+1=x-1+1=x, x\in \R$$

$$g(f(x))=\sqrt[3]{(x^3+1)-1}=\sqrt[3]{x^3}=x, x\in \R$$

Therefore the functions$f$ and $g$ are inverse functions.