Question

evaluate the compositions indicated for the given functions.

(f(x) = -2x^3), (g(x) = x^2 + 3x - 8), (h(x) = 5x)

(f(g(h(-1))))

-16
-12
10
16

Explanation:

⚡ Using what you learned: Evaluating Composite Functions

Step 1: Evaluate the innermost function

$$ h(x) = 5x $$

$$ h(-1) = 5(-1) = -5 $$

Step 2: Evaluate the middle function

$$ g(x) = x^2 + 3x - 8 $$

$$ g(h(-1)) = g(-5) = (-5)^2 + 3(-5) - 8 $$

$$ g(-5) = 25 - 15 - 8 = 2 $$

Step 3: Evaluate the outermost function

$$ f(x) = -2x^3 $$

$$ f(g(h(-1))) = f(2) = -2(2)^3 $$

$$ f(2) = -2(8) = -16 $$

Answer:

-16