Question

Find the Inverse Function:

y=4x-x^2

Answer 1

You were given:

y = 4x - x^2

We switch x and y.

x = 4y - y^2

Factor the right side of the equation.

x = y(4 - y)

Next:

xy = 4 - y

Add y on both sides of the equation.

xy + y = 4

Factor on the left side.

y(x + 1) = 4

Isolate y on the left side.

y = 4/(x + 1)

Replace y by f^-1 (x).

f^-1 (x) = 4/(x + 1)

Done!

Answer 2

How did you go from here:

x = y(4 - y)

To here:

Next:

xy = 4 - y

Shouldn't you divide rather than multiply?

Answer 3

Mike,

After doing the question again, I realize that 4x - x^2 is not one-to-one. Hence, it has no inverse function.

Sorry....The answer is: NO INVERSE FUNCTION HERE.