Find th inverse function of the equation

Question

 

f (x) = (9x+9)/7x

Answer 1

Replace f(x) by y:

 

y = (9x+9)/(7x)   (I assume the denominator is 7x.)

 

Exchange x and y (replace y by x and x by y):

 

x = (9y+9)/(7y)

 

Now, use algebra to solve for y in terms of x only: (several steps shown)

 

(7y)x = 9y+9   (multiplied both sides by 7y to clear the denominator)

 

7xy = 9y + 9    (multiply)

 

7xy - 9y = 9     (move the 9y term to the left side)

 

y(7x - 9) = 9     (factor out the common factor of y in preparation of solving for it)

 

y = 9/(7x - 9)    (divide by the other factor to solve for y)

 

Finally, replace y by f^-1(x) to use proper notation:

 

f^-1(x) = 9/(7x - 9).

 

You can check this is correct by putting one function into the other, simplifying, and verifying that you get x both times (I will not show this for you):

 

f(f^-1(x)) = x and f^-1(f(x)) = x.

 

This will PROVE that you have found the correct inverse.