If f(x)=-4x^2 and g(x)=2/x, find [g*f](x).
answer I got: [g*f](x)=g(f(x))
=g(2/-4x)^2
Is this right?
f(x)=-4x^2
g(x)=2/x
so g(f(x))= 2/(-4x^2)=-1/2x^2
I am wondering why you titled this Precalculus with applications? This problem is certainly content for algebra II. Is someone playing with course names again?
The course i am taking is Advanced Mathematical Concepts/Precalculus with Applications. Thank for your help.
No, the answer you provided is not correct. To find the composition [g * f](x), you need to substitute the function f(x) into g(x). Let's break it down step by step:
1. Start with the function g(x) = 2/x.
2. Substitute f(x) = -4x^2 into the function g(x):
g(f(x)) = 2 / (-4x^2)
3. Simplify the expression:
g(f(x)) = -1 / (2x^2)
So, the correct answer is [g * f](x) = -1 / (2x^2).