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Find an equation for this inverse.

f(x) = 5x + 1

Please help! I have a test tomorrow & I have absolutely no idea on his to do this, thanks! :)

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alphabetsam
The easiest way to find the inverse of a function is to swap the x and y, meaning:

We have the function [tex]f(x)=5x+1[/tex]. Let's call our outputs "y", so we have [tex]y=5x+1[/tex]. To find the inverse, we're going to change the x and the y's position in the equation, so we have [tex]x=5y+1[/tex]. Then all we need to do is solve for y:
[tex]x=5y+1[/tex]
[tex]x-1=5y[/tex]
[tex]\frac{x}{5}-\frac{1}{5}=y[/tex]
[tex]f^{-1}(x)=y=\frac{x}{5}-\frac{1}{5}[/tex]
budwilkins
Don you mean find its inverse function??
If so, then you can determine if a function has an inverse by passing the "horizontal line test."
This function does because it has a slope not equal to zero. Inverses of horizontal lines have vertical lines in them, which are not by definition functions.
So now, simply replace "f(x)" with "y", then switch the x and y, and solve for y:
y = 5x + 1
x = 5y + 1
-1 -1
5y = x - 1
÷5 ÷5
y = (x-1)/5

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