How would you decompose h(x) into the original functions f(x) and g(x)?

f(x) = x⁸

g(x) = -x - 6

Step-by-step explanation:

We define h(x) as the composition of f(x) and g(x), or f(g(x)).

Step 1: Define

h(x) = (-x - 6)⁸

Step 2: Rewrite

f(g(x)) = (-x - 6)⁸

Here we see that we plugged in g(x) as x into f(x). The easiest way to find f(x) and g(x) separate is to unplug g(x) from f(x).

In this case, we can see that g(x) can be set to -x - 6.

Step 3: Unsubstitute

g(x) = -x - 6

f(g(x)) = (-x - 6)⁸

f(x) = x⁸

We can tell that if we substitute back in g(x), we would get f(g(x)), or h(x), again.

Step 4: Check

f(x) = x⁸

g(x) = -x - 6

f(g(x)) = h(x) = (-x - 6)⁸

Hey there!

Note that h(x) makes up f(x) and g(x).

We are given h(x) = (-x - 6)^8

We can rewrite the composition since g(x) = -x - 6 and we can take it out by the following;

h(x) = (-x - 6)^8 -> f(x) = x^8

If we put g(x) back in, we get h(x) or f(g(x)) = (-x - 6)^8. Thus, proves the decomposition is correct.

Best of Luck!

$8

step-by-step explanation:

it is pretty much backwards.

you take the 4x2 multiply that, and that is = $8