Given functions `f(x) = 2x + 1 and g(x) = x^(2) - 4`, what is the value of `f(g(-3))`?

Options

A. `-29`
B. `-25`
C. `-19`
D. `11`

Answer

To find the value of \( f(g(-3)) \) given the functions \( f(x) = 2x + 1 \) and \( g(x) = x^2 - 4 \), we can follow these steps:

### Step 1: Calculate \( g(-3) \)
We start by substituting \(-3\) into the function \( g(x) \).

\[ g(-3) = (-3)^2 - 4 \]

Calculating \((-3)^2\):

\[ (-3)^2 = 9 \]

Now substituting back into the equation:

\[ g(-3) = 9 - 4 = 5 \]

### Step 2: Calculate \( f(g(-3)) \)
Now that we have \( g(-3) = 5 \), we need to find \( f(5) \).

Substituting \( 5 \) into the function \( f(x) \):

\[ f(5) = 2(5) + 1 \]

Calculating \( 2(5) \):

\[ 2(5) = 10 \]

Now substituting back into the equation:

\[ f(5) = 10 + 1 = 11 \]

### Final Answer
Thus, the value of \( f(g(-3)) \) is:

\[ \boxed{11} \]