Question

True or False. The domain of the composite function$\left(f\circ g\right)\left(x\right)$is the same as the domain of$g\left(x\right)$.

Short answer

This statement is true.

Step-by-step solution

Step 1. Given Information.

The domain of the composite function$\left(f\circ g\right)\left(x\right)$ is the same as the domain of$g\left(x\right)$.

Step 2. Domain of a composite function.

The function $f\left(g\left(x\right)\right)=\left(f\circ g\right)\left(x\right)$

$\Rightarrow f\left(g\left(x\right)\right)=g\left(x\right)$.