Question

Which expression defines function h?

Answer 1

`h(x) = ((f)/(g))(x)`

Explanation:

Given

`f(x) = 3x^3 + 9x^2 -12x`

`g(x) = x - 1`

`h(x) = 3x^2 + 12x`

Required

What defines h(x)

Looking at the degree of f(x), g(x) and h(x), we have:

`h(x) = ((f)/(g))(x)`

See proof

`h(x) = ((f)/(g))(x)`

This gives:

`h(x) = (f(x))/(g(x))`

`h(x) = (3x^3 + 9x^2 -12x)/(x - 1)`

Factorize

`h(x) = ((3x^2 + 12x)(x - 1))/(x - 1)\\`

`h(x) = 3x^2 + 12x`