To find the inverse of the function [tex]\( f(x) = x + 3 \)[/tex], follow these steps:
1. Rewrite the function as an equation with [tex]\( y \)[/tex]:
[tex]\[ y = x + 3 \][/tex]
2. Interchange the roles of [tex]\( x \)[/tex] and [tex]\( y \)[/tex]: Since we are finding the inverse, we swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
[tex]\[ x = y + 3 \][/tex]
3. Solve for [tex]\( y \)[/tex]: Isolate [tex]\( y \)[/tex] on one side of the equation to express it in terms of [tex]\( x \)[/tex].
[tex]\[ y = x - 3 \][/tex]
4. Express the inverse function: Replace [tex]\( y \)[/tex] with [tex]\( h(x) \)[/tex] to denote the inverse function.
[tex]\[ h(x) = x - 3 \][/tex]
So, the inverse of the function [tex]\( f(x) = x + 3 \)[/tex] is:
[tex]\[ h(x) = x - 3 \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{h(x) = x - 3} \][/tex]
