Question

If $f\left(x\right)=2x$ and $g$ is identity function, then:

• A. $\left(fog\right)\left(x\right)=g\left(x\right)$
• B. $\left(gog\right)\left(x\right)=g\left(x\right)$
• C. $\left(fog\right)\left(x\right)=(g+g)\left(x\right)$
• D. $\left(fog\right)\left(x\right)=(f+f)\left(x\right)$

Answer 1

The correct option is C

$\left(fog\right)\left(x\right)=(g+g)\left(x\right)$

Explanation for the correct option.

$g$ is identity function, so $g\left(x\right)=x$.

Now,

$\begin{array}{rcl}\left(fog\right)\left(x\right)& =& 2\left(g\right(x\left)\right)\\ & =& \left(g+g\right)x\end{array}$

Hence, option C is correct.