Question

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

Short answer

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

Step-by-step solution

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.