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Let \[f(x) = \frac{3x - 7}{x + 1}.\] Find the inverse $f^{-1}(x)$.

 Mar 18, 2018
 #1
avatar+100588 
+3

\(f(x) = \frac{3x - 7}{x + 1}\)

 

Write

 

y  =  [ 3x - 7]  /   [ x + 1]       get x by itself

y [ x + 1]  = 3x - 7

yx + y  =  3x - 7

y + 7  =  3x - yx

y+ 7  =  x (3 - y)

 

[y + 7 ] / [ 3 - y ]  =  x     "swap" x and y

 

[ x + 7 ] / [ 3 - x ]   = y   =  f-1(x)

 

 

cool cool cool

 Mar 18, 2018
 #2
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What is the inverse?

Guest Mar 18, 2018

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