How do you find the inverse of f of x equals 4 divided by the value of x - 2 squared?

Answer 1

2

Answer 2

f(x) = 4/(x-2)2 can be written y = 4/(x-2)2. The first step to finding the inverse of a function is to replace every y with an x and every x with a y, like this: x = 4/(y-2)2. Now it is good form to solve for y.

x = 4/(y-2)2

x(y-2)2 = 4

(y-2)2 = 4/x

y-2 = sqrt(4/x)

y = sqrt(4/x) + 2

So the inverse is f-1(x) = sqrt(4/x) + 2. And a plus or minus sign in front of the square root will graph both parts.