To solve the problem and find the value of [tex]\( f(1) \)[/tex] for the given function [tex]\( f(x) = 2 \cdot 2^x + 1 \)[/tex], follow these steps:
1. Substitute [tex]\( x = 1 \)[/tex] into the function:
We start by substituting the value of [tex]\( x \)[/tex] with 1 in the given function:
[tex]\[
f(1) = 2 \cdot 2^1 + 1
\][/tex]
2. Simplify the expression inside the function:
First, calculate the exponent part:
[tex]\[
2^1 = 2
\][/tex]
3. Multiply the result by 2:
Now multiply the result from the exponentiated term by 2:
[tex]\[
2 \cdot 2 = 4
\][/tex]
4. Add 1 to the result:
Finally, add 1 to the product obtained in the previous step:
[tex]\[
4 + 1 = 5
\][/tex]
Therefore, the value of [tex]\( f(1) \)[/tex] is:
[tex]\[
f(1) = 5
\][/tex]
