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).