Question

Find f(g(x)). Can you please advise if I am correct?

Answer 1

Given the following functions:

$\begin{gathered} f(x)=\sqrt{x+2} \\ g(x)=8x-6 \end{gathered}$

We will find the composite function f(g(x))

So, we will substitute the function (g) into the function (f) as follows:

$f\mleft(g\mleft(x\mright)\mright)=\sqrt{(8x-6)+2}$

Simplify the expression:

$\begin{gathered} f\mleft(g\mleft(x\mright)\mright)=\sqrt{8x-4} \\ f\mleft(g\mleft(x\mright)\mright)=\sqrt{4(2x-1)} \\ f\mleft(g\mleft(x\mright)\mright)=2\sqrt{2x-1} \end{gathered}$

so the answer will be option 3:

$f\mleft(g\mleft(x\mright)\mright)=2\sqrt{2x-1}$