Question

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

Answer 1

Given the following functions:

`\begin{gathered} f(x)=√(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)=√((8x-6)+2)`

Simplify the expression:

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

so the answer will be option 3:

`f\mleft(g\mleft(x\mright)\mright)=2√(2x-1)`