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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

Best Answer 

 #1
avatar+88769 
+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
avatar+88769 
+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

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