Question

There is much available about finding inverse function of y=f(x) but where can I find a discussion of how to find and plot inverse function 1/y = f(x). Specific example is y'=(1/y)=4+2 x. This example is from Montgomery intro to linear regression analysis 5th edition, problem 5.8. Thank you.

Mary Marion

Answer 1

Inverse of a function exist only if its a one to one function. A one ­to­ one function is a function where each input (x­value) has a unique output (y­ value). To put it another way, every time we plug in a value of x we will get a unique value of y, the same y ­value will never appear more than once. A one­ to­one function is special because only one ­to ­one functions have an inverse function.

Inverse functions are not reciprocal. f-(x) is not equal to 1/f(x)

Linear functions are all one to one function and hence there exist a inverse for them

y=4+2x

(y-4)/2 =x

or f-1(x)= (y-4)/2

In other words we will put y values in the equation to derive the x values