Posted by **kristie** on Tuesday, July 11, 2006 at 9:53am.

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?

## Answer this Question

## Related Questions

- Math - Find inverse of f if f(x)= x^2-4x+3, (for x is smaller than and equal to ...
- Pre-caluclus - I do not know how to solve for y to get the inverse of this ...
- math - Could you show me step by step how to find the inverse of this problem: ...
- Inverse of log function - Find the inverse of f(x) = log(2+x) - 4 the base is "a...
- Algebra 2 - Find the inverse of the following function: f(x) = 3x + 12 I don't ...
- Algebra - If f(x)=x^5-1/3, find f^-1(-31/96). I think the first step would be ...
- algebra/trig - 1. f(x)=x^3+5 does f(x) have an inverse? if so, find the inverse ...
- Algebra - How do you find the inverse of functions? for example how would you ...
- inverse - If f(x)=cosx + 3 how do I find f inverse(1)? Thanks y = cos(x) + 3 the...
- Advanced Algebra - What is the inverse of each of the functions defined by the ...