Question

Let f(x)=x ^3 4,g(x)=x ^2−3, and h(x)=5x 7. find the rule for the function. gf

Answer 1

The rule for the function gf is f(g(x)) = (x^2 - 3)^3 + 4.

Step-by-step explanation:

To find the rule for the function gf, we need to substitute the function g(x) into f(x). First, let's write out the function g(x) as x^2 - 3, and the function f(x) as x^3 + 4. Now, substitute g(x) into f(x): f(g(x)) = (x^2 - 3)^3 + 4. Simplifying further, we can expand the cube: f(g(x)) = (x^2 - 3)(x^2 - 3)(x^2 - 3) + 4. The rule for the function gf is f(g(x)) = (x^2 - 3)^3 + 4.