Q. 5 - Precalculus Enhanced with Graphing Utilities

Question

True or False $f\left(g\left(x\right)\right)=f\left(x\right).g\left(x\right)$.

Step-by-Step Solution

Answer

$f\left(g\left(x\right)\right)=f\left(x\right).g\left(x\right)$ is false statement.

Step 1. Given Information.

The given statement is $f\left(g\left(x\right)\right)=f\left(x\right).g\left(x\right)$.

Step 2. Definition of composite functions

Given two functions f and g, the composite function, denoted by $f\circ g$ (read as “f composed with g”), is defined by  $\left(f\circ g\right)\left(x\right)=f\left(g\left(x\right)\right)$.

So, $f\left(g\right(x\left)\right)=f\left(x\right).g\left(x\right)$ is false.