To find the inverse of the function \( f(x) = x + 3 \), we need to follow these steps:
1. Set the function equal to \( y \):
[tex]\[
y = x + 3
\][/tex]
2. Swap \( x \) and \( y \):
[tex]\[
x = y + 3
\][/tex]
3. Solve for \( y \) to express \( y \) in terms of \( x \):
[tex]\[
y = x - 3
\][/tex]
So, we have determined that the inverse function is \( h(x) = x - 3 \).
Upon comparing this with the provided options:
- \( h(x) = \frac{1}{3}x + 3 \)
- \( h(x) = \frac{1}{3}x - 3 \)
- \( h(x) = x - 3 \)
- \( h(x) = x + 3 \)
The correct inverse function is \( h(x) = x - 3 \). Therefore, the correct option is:
[tex]\( h(x) = x - 3 \)[/tex].
