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

##### 1 Answer

Aug 19, 2016

#### 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#