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Let f(x)= (3x-7)/(x+1).

 

find the inverse of f^-1(x)

 

thanks :D

WhichWitchIsWhich  Nov 6, 2017

Best Answer 

 #1
avatar+5261 
+1

f(x)  =  \(\frac{3x-7}{x+1}\)                    Let's say...

 

y  =  \(\frac{3x-7}{x+1}\)                               Now we want to solve for  x .

                                                Multiply both sides of the equation by  x + 1 .

y(x + 1)  =  3x - 7

                                                Distribute the  y .

yx + y  =  3x - 7

                                                Subtract  3x  from both sides.

yx - 3x +  y  =  -7

                                                Factor  x  out of the first two terms.

x(y - 3) + y  =  -7

                                                Subtract  y  from both sides.

x(y - 3)  =  -y - 7

                                                Divide both sides by  y - 3 .

x  =  \(\frac{-y-7}{y-3}\)

                                      Now to get the inverse, swap  x  and  y .

y  =  \(\frac{-x-7}{x-3}\)                    This is the inverse function.

 

f-1(x)  =  \(\frac{-x-7}{x-3}\)

hectictar  Nov 6, 2017
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1+0 Answers

 #1
avatar+5261 
+1
Best Answer

f(x)  =  \(\frac{3x-7}{x+1}\)                    Let's say...

 

y  =  \(\frac{3x-7}{x+1}\)                               Now we want to solve for  x .

                                                Multiply both sides of the equation by  x + 1 .

y(x + 1)  =  3x - 7

                                                Distribute the  y .

yx + y  =  3x - 7

                                                Subtract  3x  from both sides.

yx - 3x +  y  =  -7

                                                Factor  x  out of the first two terms.

x(y - 3) + y  =  -7

                                                Subtract  y  from both sides.

x(y - 3)  =  -y - 7

                                                Divide both sides by  y - 3 .

x  =  \(\frac{-y-7}{y-3}\)

                                      Now to get the inverse, swap  x  and  y .

y  =  \(\frac{-x-7}{x-3}\)                    This is the inverse function.

 

f-1(x)  =  \(\frac{-x-7}{x-3}\)

hectictar  Nov 6, 2017

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