Question

Find f(g(x)) and g(f(x)) 1. F(x) = X²-3x+1 g(x)=5x-7

Answer 1

We are given the following functions

`\begin{gathered} f(x)=x^2-3x+1 \\ g(x)=5x-7 \end{gathered}`

Let us first find f(g(x)

Substitute x = 5x - 1 into the function f(x) and simplify

`\begin{gathered} f(g(x))=(5x-7)^2-3(5x-7)+1 \\ f(g(x))=(25x^2-2\cdot5x\cdot7+49)^{}-15x+21+1 \\ f(g(x))=25x^2-70x+49^{}-15x+22 \\ f(g(x))=25x^2-70x-15x+49+22 \\ f(g(x))=25x^2-85x+71 \end{gathered}`

Now let us find g(f(x))

Substitute x = x² - 3x + 1 into the function g(x) and simplify

`\begin{gathered} g(f(x))=5(x^2-3x+1)-7 \\ g(f(x))=5x^2-15x+5-7 \\ g(f(x))=5x^2-15x-2 \end{gathered}`

Therefore, f(g(x) and g(f(x)) are

`\begin{gathered} f(g(x))=25x^2-85x+71 \\ g(f(x))=5x^2-15x-2 \end{gathered}`