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

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

find the inverse of f^-1(x)

thanks :D

WhichWitchIsWhich  Nov 6, 2017

#1
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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
Sort:

#1
+6266
+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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