SOLUTION: how do you get the inverse of y=2/x

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Question 279635: how do you get the inverse of y=2/x
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
equation is y = 2/x

solve for x.

multiply both sides of the equation by x to get:

xy = 2

divide both sides of the equation by y to get:

x = 2/y

replace x with y and y with x to get:

y = 2/x

this equation is the inverse of itself.

your equation is y = 2/x

the inverse equation is y = 2/x

A graph of your equation and the line y = x looks like this:

based on the graph, your equation looks like it is symmetric with respect to the line y = x

let's set y equal to f(x) in the original equation of y = 2/x.

y = 2/x becomes f(x) = 2/x.

let's set y equal to g(x) in the inverse equation of y = 2/x.

y = 2/x becomes g(x) = 2/x.

now we can distinguish between them.

f(x) = 2/x is the original equation.
g(x) = 2/x is the inverse equation.

the fact that they represent the same equation is an anomaly of the inverse function rules but the rules still hold.

if they are truly inverse equations of each other, then for every x in f(x), we should have g(f(x)) = x.

to see if that's true, let's do the following:

let x = 6.

f(x) = 2/x = 2/6 = 1/3

since f(x) = 1/3, then g(f(x)) = g(1/3).

since g(x) = 2/x, then g(1/3) = 2 / (1/3) which equals 6.

we simply replace x with 1/3 in the equation.

there we have it.

g(f(x)) = x

x = 6
f(x) = 1/3
g(1/3) = 6

the test for inverse function is passed and this function is the inverse function of itself.