Questions: Suppose f(x)=4-x^2 and g(x)=2x+5. Find the value of f(g(-2)).

Transcript text: Suppose $f(x)=4-x^{2}$ and $g(x)=2 x+5$. Find the value of $f(g(-2))$. 5 3 $-8$ 0

Solution

Step 1: Evaluate $ g(-2) $

Given $ g(x) = 2x + 5 $, substitute $ x = -2 $: \[ g(-2) = 2(-2) + 5 = -4 + 5 = 1 \]

Step 2: Substitute $ g(-2) $ into $ f(x) $

Given $ f(x) = 4 - x^2 $, substitute $ x = g(-2) = 1 $: \[ f(g(-2)) = f(1) = 4 - (1)^2 = 4 - 1 = 3 \]

Step 3: Final Result

The value of $ f(g(-2)) $ is: \[ f(g(-2)) = 3 \]

$\boxed{3}$

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