Answer:
[tex] - 2x - h[/tex]
Step-by-step explanation:
We are given a function [tex]g(x)=2-x^2[/tex]. We want to find [tex](g(x+h)-g(x))/h[/tex] To do so, first we need to work out the numerator
[tex]g(x+h)=2-(x+h)^2[/tex]. Therefore
[tex]g(x+h)-g(x)\implies 2-x^2-2xh-h^2-2x-x^2[/tex]
like terms cancel out leaving us with
So,
[tex] \displaystyle\frac{g(x + h) + g(x)}{h} = \frac{ h( - 2x - h )}{h} = \boxed{ - 2x - h}[/tex]
