Question

Let f(x) = 3x – 3 and g(x) = x + 5. Find f(g(x)) and g(f(x)).

Answer 1

given data:

`\begin{gathered} f\mleft(x\mright)=3x-3 \\ g\mleft(x\mright)=x+5 \end{gathered}`

to find:

`f\mleft(g\mleft(x\mright)\mright)\text{ and }g\mleft(f\mleft(x\mright)\mright)`
`\begin{gathered} g(x)=x+5 \\ =f(x+5) \\ =3(x+5)-3 \\ =3x+12 \end{gathered}`
`\begin{gathered} f(x)=3x-3 \\ =g(3x-3) \\ =(3x-3)+5 \\ =3x+2 \end{gathered}`