ANSWER
The inverse is
[tex]f ^{ - 1} (x) = x + 5[/tex]
EXPLANATION
The given function is
[tex]f(x) = x - 5[/tex]
To find the inverse of this function, we let
[tex]y = f(x)[/tex]
This implies that,
[tex]y = x - 5[/tex]
We now interchange x and y to obtain,
[tex]x = y - 5[/tex]
We make y the subject again by adding 5 to both sides to get,
[tex]x + 5 = y - 5 + 5[/tex]
This implies that,
[tex]x + 5 = y[/tex]
or
[tex]y = x + 5[/tex]
This new function is the inverse of the given function.
Therefore
[tex]f ^{ - 1} (x) = x + 5[/tex]
