Question

How do you find `(g@f)(-2+x)` given `g(x)=2x-2` and `f(x)=x^2+3x`?

Answer 1

`2x^2-2x-6`

Explanation:

The first step is to find an expression for (g ￮ f ), which can also be written as g(f(x)).

To do this substitute x = f(x) into g(x)

`rArrg(f(x))=g(color(red)(x^2+3x))=2(color(red)(x^2+3x))-2`

`rArrg(f(x))=2x^2+6x-2`

To evaluate (g ￮ f)(-2 +x) substitute x = - 2 +x into g(f(x))

`rArr(g(f(color(magenta)(-2+x)))=2(color(magenta)(-2+x))^2+6(color(magenta)(-2+x))-2`

`=2(4-4x+x^2)-12+6x-2`

`=8-8x+2x^2-12+6x-2=2x^2-2x-6`