Let f(x)= 2x^2, g(x)= 5x-6, and m(x)= 3x. Find and simplify the composite function g(m(f(x))).
g(m(f)) = g(3f) = 5(3f)-6 = 15f-6 = 15(2x^2)-6 = 30x^2 - 6
THANKS STEVE, I REALLY APPRECIATE THE HELP!!
To find the composite function g(m(f(x))), we need to plug in f(x) into m(x), and then plug the result into g(x).
First, let's find f(x):
f(x) = 2x^2
Then, let's find m(f(x)):
m(f(x)) = m(2x^2)
= 3(2x^2)
= 6x^2
Now, let's find g(m(f(x))):
g(m(f(x))) = g(6x^2)
= 5(6x^2) - 6
= 30x^2 - 6
So, the simplified composite function g(m(f(x))) is 30x^2 - 6.