Given the function f(x)= x+1/x-3 Find the inverse of f(x). (use parenthesis to type your answer)

zandaleebailey
Mar 4, 2015

#1**+10 **

We want to get x by itself.......so we have

y = (x + 1) / (x - 3) multiply both sides by x -3

y(x - 3) = x + 1 simplify

yx - 3y = x + 1

yx - x = 1 + 3y

x(y - 1) = 1 + 3y

x = (1 + 3y) / (y - 1) "exchange" x and y

y = (1 + 3x) / (x - 1) for "y," write f^{-1}(x)

f^{-1}(x) = (1 + 3x) / (x - 1)

Here's the graph of f(x) and f^{-1}(x).....

https://www.desmos.com/calculator/t7vncorptl

CPhill
Mar 4, 2015

#1**+10 **

Best Answer

We want to get x by itself.......so we have

y = (x + 1) / (x - 3) multiply both sides by x -3

y(x - 3) = x + 1 simplify

yx - 3y = x + 1

yx - x = 1 + 3y

x(y - 1) = 1 + 3y

x = (1 + 3y) / (y - 1) "exchange" x and y

y = (1 + 3x) / (x - 1) for "y," write f^{-1}(x)

f^{-1}(x) = (1 + 3x) / (x - 1)

Here's the graph of f(x) and f^{-1}(x).....

https://www.desmos.com/calculator/t7vncorptl

CPhill
Mar 4, 2015