Question

Given two functions (x) and g(x),SC) = 8x - 5,8(x) = 2x2 + 8Step 2 of 2: Form the composition g(x)).Answer 2 PointsKeypadKeyboard Shortcuts&(()) =NG

Answer 1

We have to find the composition of functions g(f(x)).

We have the definitions of f(x) and g(x) as:

`\begin{gathered} f(x)=8x-5 \\ g(x)=2x^2+8 \end{gathered}`

Then, we can find the composition as;

`\begin{gathered} g(f(x))=2f(x)^2+8 \\ g(f(x))=2(8x-5)^2+8 \\ g(f(x))=2((8x)^2-2\cdot5\cdot8x+(-5)^2)+8 \\ g(f(x))=2(64x^2-80x+25)+8 \\ g(f(x))=128x^2-160x+50+8 \\ g(f(x))=128x^2-160x+58 \end{gathered}`

Answer: g(f(x)) = 128x² - 160x +58