Question

Which expression represents the composition [g o f o h](x) for the functions below?

f(x) = 5x – 4
g(x) = 5x^3
h(x) = 3x

5(15x – 4)^3
(75x – 20)^3
5(5x – 4)^3
675x^3 – 4

Answer 1

To find the composition [g \circ f \circ h](x), apply h(x) = 3x, then f(h(x)) = 15x - 4, and finally g(f(h(x))) = 5(15x - 4)^3.

Step-by-step explanation:

To find the composition [g \circ f \circ h](x), we need to apply each function in the correct order. First, we apply h to x, then f to h(x), and finally g to f(h(x)).

Start with h(x) = 3x.

Apply f to h(x): f(h(x)) = 5(3x) - 4 = 15x - 4.

Apply g to f(h(x)): g(f(h(x))) = 5(15x - 4)3.

This gives us the final expression for the composition as 5(15x - 4)3.

Answer 2

A

5(15x-4)^3

Step-by-step explanation:

I assume you mean g(f(h(x))) so in that case here is how you do it:

So the first one is g(x) which is:

5x^3

Now g(f(x)) you just plug in f(x) for the x in the g equation. It would look like this:

5(5x-4)^3

Now the h(x) you would do the same, plug it in for all the values of x in g(x). So it would look like this:

5(5(3x)-4)^3

Since you simplify, you get 5(15x-4)^3

This final equation is g(f(h(x))) which is what you were looking for, which is A