To find the inverse of the function [tex]\( f(x) = x + 5 \)[/tex], we follow a series of steps:
1. Replace [tex]\( f(x) \)[/tex] with [tex]\( y \)[/tex]:
[tex]\[ y = x + 5 \][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse function equation:
[tex]\[ x = y + 5 \][/tex]
3. Solve the equation for [tex]\( y \)[/tex]:
[tex]\[ x - 5 = y \][/tex]
4. Replace [tex]\( y \)[/tex] with [tex]\( f^{-1}(x) \)[/tex]:
[tex]\[ y = x - 5 \][/tex]
So, filling in the blanks in the steps provided:
1. [tex]\( y \)[/tex] [tex]\( = x + 5 \)[/tex]
2. [tex]\( x \)[/tex] [tex]\( = y + 5 \)[/tex]
3. [tex]\( x - 5 \)[/tex] [tex]\( = y \)[/tex]
4. [tex]\( y \)[/tex] [tex]\( = x - 5 \)[/tex]
Thus, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[ f^{-1}(x) = x - 5 \][/tex]
