To find the inverse of the function [tex]\( f(x) = x + 5 \)[/tex], let's follow a step-by-step approach:
1. First, express the function:
[tex]\[
f(x) = x + 5
\][/tex]
2. Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[
y = x + 5
\][/tex]
3. Solve for [tex]\( x \)[/tex] in terms of [tex]\( y \)[/tex]:
[tex]\[
x = y - 5
\][/tex]
4. Write the inverse function:
[tex]\[
f^{-1}(y) = x - 5
\][/tex]
Now let's complete the steps using the given framework:
1. [tex]\( f(x) = x + 5 \)[/tex]
2. [tex]\( y = x + 5 \)[/tex]
3. [tex]\( x = y - 5 \)[/tex]
4. [tex]\( f^{-1}(y) = x - 5 \)[/tex]
The functions have been clearly transformed to solve for the inverse step by step.
