To find the values of the function [tex]\( f(x) = 2^{x-1} \)[/tex] at specific points, follow these steps:
1. Calculate [tex]\( f(3) \)[/tex]:
- Substitute [tex]\( x = 3 \)[/tex] into the function [tex]\( f(x) \)[/tex].
- So, [tex]\( f(3) = 2^{3-1} \)[/tex].
- Simplify the exponent: [tex]\( 3 - 1 = 2 \)[/tex].
- Thus, [tex]\( f(3) = 2^2 \)[/tex].
- Calculate [tex]\( 2^2 \)[/tex]: [tex]\( 2 \times 2 = 4 \)[/tex].
Therefore, [tex]\( f(3) = 4 \)[/tex].
2. Calculate [tex]\( f(5) \)[/tex]:
- Substitute [tex]\( x = 5 \)[/tex] into the function [tex]\( f(x) \)[/tex].
- So, [tex]\( f(5) = 2^{5-1} \)[/tex].
- Simplify the exponent: [tex]\( 5 - 1 = 4 \)[/tex].
- Thus, [tex]\( f(5) = 2^4 \)[/tex].
- Calculate [tex]\( 2^4 \)[/tex]: [tex]\( 2 \times 2 \times 2 \times 2 = 16 \)[/tex].
Therefore, [tex]\( f(5) = 16 \)[/tex].
In summary:
[tex]\[
\begin{align*}
f(3) &= 4 \\
f(5) &= 16
\end{align*}
\][/tex]
