Let g be the function defined by the equation below

Question

g(x)=-x² + 10x

Find

g (a+h)

g(-a)

a + g(a)

 

Answer 1

Anything that is in parentheses, substitute that into x. Then simplify the following expressions.

 

g(a+h) = -(a + h)² + 10(a + h)

           = -(a² + 2ah + h²) + 10a + 10h

           = -a² - 2ah - h² + 10a + 10h

            

g(-a) = -(-a)² + 10(-a)

        = -a² - 10a

        = -a(a + 10)

        

a + g(a) = a +[-a² + 10a]

             = a - a² + 10a

             = 11a - a²