f(x) = 3x^2 , g(x) = 3x-1, and m(x) = 4x
Find and simplify the composition function g(m(f(x)))
answers i got which were wrong
3x-1(12x^3)
36x^4-12x^3
Maybe i am putting the information in incorrectly..
Should it look like this (3x^2(4x(3x^2))) then solve?
m(x) = 4x, so
m(f) = 4f = 12x^2
g(x) = 3x-1, do
g(m) = 3m-1 = 36x^2-1
Using your nested notation,
g(m(f(x)) = 3(m(f(x))-1
= 3(4(f(x))-1
= 3(4(3x^2))-1
=36x^2-1
To find the composition function g(m(f(x))), we need to first evaluate f(x), then substitute that result into m(x), and finally substitute the result from m(x) into g(x). Let's break it down step by step:
1. Evaluate f(x):
f(x) = 3x^2
2. Substitute the result from f(x) into m(x):
m(x) = 4x
m(f(x)) = 4(3x^2) = 12x^2
3. Substitute the result from m(f(x)) into g(x):
g(x) = 3x - 1
g(m(f(x))) = g(12x^2) = 3(12x^2) - 1 = 36x^2 - 1
Therefore, the composition function g(m(f(x))) simplifies to 36x^2 - 1.