[tex]f(x)=5x\to y=5x[/tex]
change x to y, and y to x
[tex]x=5y[/tex]
solve for y:
[tex]5y=x\ \ \ |:5\\\\y=\dfrac{x}{5}\to y=\dfrac{1}{5}x[/tex]
Answer:
[tex]f^{-1}(x)=\dfrac{1}{5}x[/tex]
Please, take just a little more time and write the label "inverse function" like this:
-1
f (x). We want the inverse function of f(x) = 5x.
How to obtain it:
1) replace f(x) by y.
2) interchange x and y: x = 5y
3) solve this result for y: y = x/5
4) replace y with the correct symbol for "inverse function of f:"
-1
f (x) = x/5 (answer)