Questions: If f(x)=2x-2 and g(x)=x^2+1, then f(g(-2))= -. a.) 4 b.) 8 c.) - 12 d.) -8

Transcript text: If $f(x)=2 x-2$ and $g(x)=x^{2}+1$, then $f(g(-2))=$ $\qquad$ -. a.) 4 b.) 8 c.) - 12 d.) -8

Solution

Step 1: Evaluate $ g(-2) $

First, we need to find the value of $ g(-2) $. The function $ g(x) $ is given by:

\[ g(x) = x^2 + 1 \]

Substitute $ x = -2 $ into the function:

\[ g(-2) = (-2)^2 + 1 = 4 + 1 = 5 \]

Step 2: Evaluate $ f(g(-2)) $

Now that we have $ g(-2) = 5 $, we need to find $ f(g(-2)) = f(5) $. The function $ f(x) $ is given by:

\[ f(x) = 2x - 2 \]

Substitute $ x = 5 $ into the function:

\[ f(5) = 2(5) - 2 = 10 - 2 = 8 \]

The value of $ f(g(-2)) $ is $\boxed{8}$. Therefore, the answer is b.) 8.

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