To calculate the function values for [tex]\( f(x) = 2^{x-2} \)[/tex], we need to substitute the values for [tex]\( x \)[/tex] into the given function.
1. Calculate [tex]\( f(3) \)[/tex]:
- Start by substituting [tex]\( x = 3 \)[/tex] into the function:
[tex]\[
f(3) = 2^{3-2}
\][/tex]
- Simplify the exponent:
[tex]\[
3 - 2 = 1
\][/tex]
- Therefore, the expression becomes:
[tex]\[
f(3) = 2^1
\][/tex]
- Finally, calculate [tex]\( 2^1 \)[/tex]:
[tex]\[
2^1 = 2
\][/tex]
So, [tex]\( f(3) = 2 \)[/tex].
2. Calculate [tex]\( f(5) \)[/tex]:
- Start by substituting [tex]\( x = 5 \)[/tex] into the function:
[tex]\[
f(5) = 2^{5-2}
\][/tex]
- Simplify the exponent:
[tex]\[
5 - 2 = 3
\][/tex]
- Therefore, the expression becomes:
[tex]\[
f(5) = 2^3
\][/tex]
- Finally, calculate [tex]\( 2^3 \)[/tex]:
[tex]\[
2^3 = 8
\][/tex]
So, [tex]\( f(5) = 8 \)[/tex].
In summary, the calculated function values are:
[tex]\[
\begin{array}{l}
f(3) = 2 \\
f(5) = 8
\end{array}
\][/tex]
