Relations and Functions

Question

Determine g(x+a)-g(x) for the following function.

g(x)=-x^2-x

g(x+a)-g(x)=?

Thanks!

Answer 1

If g(x)=-x^2-x then

g(x+a)-g(x)=-(x+a)^2-(x+a) -(-x^2-x)=

=-(x^2+2ax+a^2)-x-a+x^2+x

=-x^2-2xa-a^2-x-a+x^2+x

=-2ax-a^2-a