Question

Given f(x)=3x 2, g(x)=(4/9x-5)-4, determine g(f(x))

Answer 1

The composite function is g(f(x)) = ⅔/3x2 - 9/4.

Step-by-step explanation:

The student is asking to find the composite function g(f(x)) where f(x) = 3x2 and g(x) = ⅔/x - 5 - 4. To determine g(f(x)), we substitute f(x) into g(x).

First, calculate f(x):
f(x) = 3x2.

Then, substitute f(x) into g(x):
g(f(x)) = g(3x2) = ⅔/(3x2) - 5 - 4.

Simplify the expression:

g(f(x)) = ⅔/3x2 - 9/4
This is achieved by first multiplying the numerator and the denominator by 3 to have a common denominator, and then combining like terms.

Therefore, the composite function is g(f(x)) = ⅔/3x2 - 9/4.