Question

Find the inverse function.

Answer 1

the inverse of nothing is nothing :{

Answer 2

\[f(x)=(x-6)/(x+5)\]

Answer 3

i couldnt type an equation in the question box sorry

Answer 4

thats ok i got it! answer to follow

Answer 5

exchange the position of the x and y variables in you original function\[x=\frac{y-6}{y+5}\]clear denominators by multiplying by y+5\[x(y+5)=y-6\]distribute on the left\[xy+5x=y-6\]collect terms with y on left side\[5x+6=y-xy\]factor out y from left side\[5x+6=y(1-x)\]divide by 1-x\[\frac{5x+6}{1-x}=y\]you can give the inverse a name such as\[f ^{-1}(x)=\frac{5x+6}{1-x}\]this is your inverse function

Answer 6

thank you. didnt think of that method.

Answer 7

FYI: one characteristic of a function and its inverse is that they are symmetric about the line y=x (see attachment); note that f^-1 is called g(x) in the sketch