Chapter 1.5, Problem 3QR

To determine

To evaluate: The value of expression $\left(f\circ g\right)\left(x\right)$ .

Answer to Problem 3QR

The value of $\left(f\circ g\right)\left(x\right)$ is ${\left(x\right)}^{2/3}$ .

Explanation of Solution

Given information: The functions are $f\left(x\right)=\sqrt[3]{x-1}$ and $g\left(x\right)=x^2+1$ .

Calculation:

Substitute $g\left(x\right)$ for $x$ in the function $f\left(x\right)=\sqrt[3]{x-1}$ .

  $\begin{array}{c}f\left(g\left(x\right)\right)=\sqrt[3]{g\left(x\right)-1}\\ =\sqrt[3]{x^2+1-1}\\ =\sqrt[3]{x^2}\\ ={\left(x\right)}^{2/3}\end{array}$

Therefore, the value of $\left(f\circ g\right)\left(x\right)$ is ${\left(x\right)}^{2/3}$ .