SOLUTION: f(x) = (2x + 3)/4 then f-1(x)

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Question 1113908: f(x) = (2x + 3)/4 then f-1(x)
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
f^-1(x) is the inverse of f(x).

your equation is f(x) = (2x+3)/4

replace f(x) with y and it becomes y = (2x+3)/4

solve for x as follows:

multiply both sides of the equation by 4 to get 4y = 2x + 3
subtract 3 from both sides of the equation to get 4y-3 = 2x
divide both sides of the equation by 2 to get (4y-3)/2 = x
now replace x with y and y with x to get (4x-3)/2 = y
switch sides to get y = (4x-3)/2.
replace y with f^-1(x) to get f^-1(x) = (4x-3)/2
that's your inverse equation.

to graph replace f(x) with y and replace f^-1(x) with y and graph both equations.
you will graph y = (2x+3)/4 and y = (4x-3)/2
your graph looks like this:

$$$

red is your normal equation.
blue is your inverse equation.

you can tell these are inverse equations of each other because they are refledtions about the line y = x and f(a,b) = f^-1(b,a).

that's evident when you look at the intersection of both lines with the line y = -x + 8, where a is equal to 4.137 and b is equal to 4.833.