Question

Find and simplify.

f(x)=7-x^2

a) f(x+h)-f(x)

b) f(x+h)-f(x)/h​

Answer 1

a)
`f(x+h)-f(x) = h(-h-2x)`

b)
`( f(x+h)-f(x))/(h)=-h-2x`

Explanation:

Our parent function is

`f(x)=7-x^2`

`f(x+h) = 7-(x+h)^2`

`= 7-(x^2+h^2+2xh)`

`=7-x^2-h^2-2xh`

`f(x+h)-f(x)= 7-x^2-h^2-2xh-(7-x^2)`

`= 7-x^2-h^2-2xh-7+x^2`

`f(x+h)-f(x) = -h^2-2xh`

taking out h as GCF

a)
`f(x+h)-f(x) = h(-h-2x)`

also

b)
`( f(x+h)-f(x))/(h)=(h(-h-2x))/(h)`

`( f(x+h)-f(x))/(h)=-h-2x`