What is the inverse function of` (2x+5)/(x+4)` ?

Expert Answers
ishpiro eNotes educator| Certified Educator

To find the inverse function, substitute x for y in the equation y = f(x), and vice versa. Then, solve the resultant equation for y.

The given function is `y = f(x) = (2x+5)/(x+4)` .

Substituting x for y and y for x results in

`x = (2y+5)/(y+4)` .

To solve this equation for y, first multiply both sides by the denominator, y + 4:

x(y+4) = 2y + 5

Open the parenthesis on the left side:

xy + 4x = 2y + 5

Now combine all terms containing y on the left side and the rest of the terms on the right side. To do that, subtract 2y and 4x from both sides:

xy - 2y = 5 - 4x

Factor out y:

y(x - 2) = 5 - 4x

Finally, to isolate y, divide both sides by x - 2:

`y = (5 - 4x)/(x - 2)`

The result is the inverse function of `f(x) = (2x+5)/(x+4)` , also denoted as

`f^(-1)(x) = (5-4x)/(x-2)` .