Question

Given the definitions of ƒ (x) and g(x) below, find the value of g(f(-3)).

f(x) = 4x +9
g(x) = 3x² − x + 4

Answer 1

g(f(-3)) = 34

Explanation:

Start with f(-3) and calculate that.

f(x) = 4x + 9

f(-3) = 4(-3) + 9

f(-3) = -12 + 9

f(-3) = -3

Next put the output, the answer for f(-3) into g(x)

(its kinda a coincidence that we put in -3 and got out -3 also. For others of these problems that you have to do, the answer to the first part won't always be the same number as the starting number!!).

g(x) = 3x^2 - x + 4

g(-3) = 3(-3)^2-(-3)+4

g(-3) = 3•9-(-3)+4

g(-3) = 27 + 3 + 4

g(-3) = 34

g(f(-3)) = 34

Answer 2

g(f(- 3)) = 34

Explanation:

substitute x = - 3 into f(x) then substitute the value obtained into g(x)

f(- 3) = 4(- 3) + 9 = - 12 + 9 = - 3 , then

g(- 3) = 3(- 3)² - (- 3) + 4 = 3(9) + 3 + 4 = 27 + 3 + 4 = 34