Question

evaluate the compositions indicated for the given functions.

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

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

-16
-12
10
16

Explanation:

⚡ Using what you learned: Evaluating Composite Functions

Step 1: Evaluate the innermost function \( f(-1) \)

Given:

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

Substitute \( x = -1 \):

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

Step 2: Evaluate the middle function \( g(f(-1)) \)

Given:

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

Substitute \( x = 2 \):

$$ g(2) = (2)^2 + 3(2) - 8 = 4 + 6 - 8 = 2 $$

Step 3: Evaluate the outermost function \( h(g(f(-1))) \)

Given:

$$ h(x) = 5x $$

Substitute \( x = 2 \):

$$ h(2) = 5(2) = 10 $$

Answer:

10