Question 380911: The function f(x)=9x+1 is one-to-one. Find the inverse
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! f(x) = 9x + 1
let y = f(x)
you get y = 9x + 1
let y = x and x = y
you get x = 9y + 1
solve for y to get y = (x-1)/9
that's your inverse function.
if it is a true inverse function, it will be a reflection of the original function about the line y = x.
to show that, then graph the functions y = x, y = 9x+1, y = (x-1)/9.
that graph is shown below:
you can pretty much eyeball it and see that the graph of y = (x-1)/9 is a reflection of y = 9x+1 about the line y = x.
a more exact interpretation is that f(x,y) in the normal equation should be equal to f(y,x) in the inverse equation.
how you find that out is as follows:
let x = 5 in the normal equation.
then you get y = 9x + 1 which becomes 46
in your normal equation, when x = 5, then y = 46
in your inverse equation, when x = 46, you should get y = 5.
the y in the normal equation becomes the x in the inverse equation.
the x in the normal equation becomes the y in the inverse equation.
when x = 46, y = (x-1)/9 becomes y = (46-1)/9 becomes y = 45/9 becomes 5.
f(x,y) = f(5,46) in your normal equation.
f(y,x) = f(46,5) in your inverse equation.
this proves they are inverse equations.
the inverse equation undoes what the normal equation does.
normal equation takes 5 and makes it 46.
inverse equation takes 46 and makes it 5.
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