To find the inverse of the function [tex]\( f(x) = x + 3 \)[/tex], follow these detailed steps:
1. Express the function in terms of [tex]\( y \)[/tex]:
[tex]\[ y = f(x) = x + 3 \][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[ x = y + 3 \][/tex]
3. Solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[ y = x - 3 \][/tex]
4. Express the inverse function [tex]\( f^{-1}(x) \)[/tex] using the solved equation:
[tex]\[ f^{-1}(x) = x - 3 \][/tex]
Therefore, the inverse function is [tex]\( f^{-1}(x) = x - 3 \)[/tex].
From the given options, the correct answer is:
[tex]\[ h(x) = x - 3 \][/tex]
