# inverse

posted by
**kristie**
.

find f^-1 (x). (this is asking me to find the inverse)

f(x) = -(x-2)^2, x <= 2

how do I solve this problem?

find f^-1 (x). (this is asking me to find the inverse)

f(x) = -(x-2)^2, x <= 2

how do I solve this problem?>>

If f(x)=-(x-2)^2 x<-2, then

let y=f(x)

- y = (x-2)^2

sqrt(-y)= x-2

x(y)= sqrt (-y) + 2

g(x)= sqrt(-x) + 2

and that is the inverse function

check:

g(f(x))= sqrt( (x-2)^2) +2 =x

f(g(x)= -((sqrt(-x) + 2 -2)^2= x

since g(f(x))=f(g(x)=x, then g(x) above is the inverse. Practice these.

I did not mean x<-2, but x is less than or equal to. How is this going to change the answer?