Question

I don’t understand this part of my homework Question 3

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given functions

`\begin{gathered} f(x)=5x+8 \\ g(x)=8x \end{gathered}`

STEP 2: Find f o g

`\begin{gathered} f\:\circ \:g=f\left(g\left(x\right)\right) \\ g\left(x\right)=8x \\ =f\left(8x\right) \\ f\left(8x\right)=40x+8 \end{gathered}`

f o g = 40x+8

STEP 3: Find g o f

`\begin{gathered} g\:\circ \:f=g\left(f\left(x\right)\right) \\ f\left(x\right)=5x+8 \\ =g\left(5x+8\right) \\ =8(5x+8) \\ =40x+64 \end{gathered}`

g o f = 40x + 64

STEP 4: Find f o f

`\begin{gathered} f\:\circ \:f=f\left(f\left(x\right)\right) \\ f\left(x\right)=5x+8 \\ =f\left(5x+8\right)=5(5x+8)+8=25x+40+8 \\ =25x+48 \end{gathered}`

f o f = 25x+48

STEP 5: Find g o g

`\begin{gathered} g\:\circ \:g=g\left(g\left(x\right)\right) \\ g\left(x\right)=8x \\ =g\left(8x\right) \\ =8(8x) \\ =64x \end{gathered}`

g o g = 64x