To solve the given problem, we are tasked with finding $f(2)$ for the function:
$f(x) = 2(3^x) + 1.$

Step 1: Substitute $x = 2$ into the function.

The equation becomes:
$f(2) = 2(3^2) + 1.$

Step 2: Evaluate $3^2$.

$3^2 = 9.$

Substitute this into the equation:
$f(2) = 2(9) + 1.$

Step 3: Simplify the expression.

First, multiply $2 \times 9$:
$2(9) = 18.$
Then add 1:
$18 + 1 = 19.$

Final Answer:

The value of $f(2)$ is 19.

Correct Option:

B. 19

Let me know if you’d like further clarification or an explanation of exponential functions!

Related Questions:

1. What is $f(3)$ for the same function $f(x) = 2(3^x) + 1$?
2. If $g(x) = 2(4^x) - 1$, what is $g(2)$?
3. How does changing the base of the exponent (e.g., from 3 to 4) affect the function $f(x)$?
4. Solve for $x$ if $f(x) = 55$ for the same function.
5. What is the graph of $f(x) = 2(3^x) + 1$?

Tip: In exponential functions, the base (like 3 in $3^x$) determines how rapidly the function grows.