Question

For the functions f(x)=4x2−3 and g(x)=2x+1, find (f∘g)(0) and (g∘f)(0).

Answer 1

To find (f∘g)(0), substitute g(x) into f(x) and evaluate at x=0. To find (g∘f)(0), substitute f(x) into g(x) and evaluate at x=0.

Step-by-step explanation:

To find (f∘g)(0), we need to perform the composition of functions f and g, and then evaluate the resulting composition function at x = 0.

First, we substitute g(x) (which is 2x+1) into f(x) to get: f(g(x)) = 4(2x+1)^2 - 3.

Next, we substitute x = 0 into the composition function to get the final result: (f∘g)(0) = 4(2(0)+1)^2 - 3 = 4(1)^2 - 3 = 4 - 3 = 1.

To find (g∘f)(0), we need to perform the composition of functions g and f, and then evaluate the resulting composition function at x = 0.

First, we substitute f(x) (which is 4x^2 - 3) into g(x) to get: g(f(x)) = 2(4x^2 - 3) + 1.

Next, we substitute x = 0 into the composition function to get the final result: (g∘f)(0) = 2(4(0)^2 - 3) + 1 = 2(-3) + 1 = -6 + 1 = -5.