Respuesta :

gmany

[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)

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