Question

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?