Question

Been stuck on this for already an hour. I need a hero..

Answer 1

h + 4

Explanation:

given

f(x) = x² - 2x + 1

then

f(3 + h)

= (3 + h)² - 2(3 + h) + 1 ← expand (3 + h)² using FOIL

= 9 + 6h + h² - 6 - 2h + 1 ← collect like terms

= h² + 4h + 4

and

f(3) = 3² - 2(3) + 1 = 9 - 6 + 1 = 4

then difference quotient

`(f(3+h)-f(3))/(h)`

=
`(h^2+4h+4-4)/(h)`

=
`(h^2+4h)/(h)` ← factor out h from each term on the numerator

=
`(h(h+4))/(h)` ← cancel h on numerator/ denominator

= h + 4