Question

$\text{The function}fog\left(x\right)\text{can be defined if}$ ___

• A. Domain of $g\left(x\right)$ $\subseteq$ Domain of $f\left(x\right)$
• B. Range of $g\left(x\right)$ $\subseteq$ Domain of $f\left(x\right)$
• C. Range of $g\left(x\right)$ $\subseteq$ Range of $f\left(x\right)$
• D. Domain of $g\left(x\right)$ $\subseteq$ Range of $f\left(x\right)$

Answer 1

The correct option is B Range of $g\left(x\right)$ $\subseteq$ Domain of $f\left(x\right)$

$\because fog\left(x\right)=f\left[g\right(x\left)\right]$
In the function $fog\left(x\right)$ the value obtained from $g\left(x\right)$ is going to be substituted the function $f\left(x\right)$.
So, the range of $g\left(x\right)$ should be with in the domain of $f\left(x\right)$.
$\therefore$ The range of $g\left(x\right)$ should be the subset of domain of $f\left(x\right)$