Given the following functions, perform the indicated operation. Then state the domain.

Question

F(x)=3x-6

g(x)=2x^2-5x

g(f(x))=?

Answer 1

Hi Kyla!

f(x) = 3x-6

g(x) = 2x² - 5x

g(f(x)) = ?

Substitute the f(x) expression into the g(x) expression (i.e. replace the x's of the g(x) function with the expression of the f(x) function):

g(f(x)) = 2(3x - 6)² - 5(3x - 6)

= 2(3x - 6)(3x - 6) - 5(3x - 6)

= 2(9x² - 36x + 36) - 15x + 30

= 18x² - 72x + 72 - 15x + 30

g(f(x)) = 18x² - 87x + 102

Domain: - ∞ < x < - ∞