Q. 6 - Precalculus Enhanced with Graphing Utilities

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 $g\left(x\right)$.

Step-by-Step Solution

Answer

This statement is true.

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

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