Answer :
For this case we have the following function:
[tex] f (x) = 5x
[/tex]
We want to find the inverse of the function.
The first thing we should do is rewrite the function:
[tex] y = 5x
[/tex]
From here, we clear the value of x.
We have then:
[tex] x =\frac{y}{5} [/tex]
Then, returning the variable changes, we have that the inverse function is:
[tex] f ^ {-1} (x) =\frac{x}{5}
[/tex]
Answer:
The inverse function of f (x) is:
[tex] f ^ {-1} (x) =\frac{x}{5}
[/tex]
An inverse function is the function which is anti function of the original function. The invers of the given function is,
[tex]f^{-1}=\dfrac{x}{5}[/tex]
In the given problem, the inverse of the function has to be find out.
What is inverse function?
An inverse function is the function which is anti function of the original function. The inverse function is the undo or reverse of the function given.
Given information-
The function given in the problem is,
[tex]f(x)=5x[/tex]
Equate the equation in terms of variable y,
[tex]y=5x[/tex]
Change both the variables as,
[tex]x=5y[/tex]
Rewrite the equation for [tex]y[/tex] as,
[tex]y=\dfrac{x}{5}[/tex]
Hence the change of variable gives the inverse of the original function. Replace [tex]y[/tex] by [tex]f^{-1}[/tex] as,
[tex]f^{-1}=\dfrac{x}{5}[/tex]
Thus the invers of the given function is,
[tex]f^{-1}=\dfrac{x}{5}[/tex]
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