# Domain of Inverse?

1. Jan 15, 2012

### FlopperJr

1. The problem statement, all variables and given/known data

The function f:x→ 4-x2 for the domain x≤0. Find the inverse of is denoted by f-1 and state the domain and range of f-1.

2. Relevant equations
Set equation to 0 and solve for x to find inverse. The D and R is going to be switched for the inverse..?

3. The attempt at a solution
I think I have found the inverse and range for this problem:
f-1(x) = -√4-x

and has a range of y≤0 (which was given in problem)

not sure of range. Are my solutions correct?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Jan 15, 2012

### SammyS

Staff Emeritus
You should really put 4-x in parentheses (or use LaTeX):
f -1(x) = -√(4-x)
The Range of f -1(x) is the same as the Domain of f(x). You are correct about this.

Do you know the Range of f(x) ?

3. Jan 16, 2012

### FlopperJr

No, That is my problem. I tried but I keep getting wrong answer. 4-x^2=0
x=+/-2

4. Jan 16, 2012

### SammyS

Staff Emeritus
How would you describe the graph of y = 4-x2 ?

5. Jan 16, 2012

### FlopperJr

Its a parabola. It opens down, with the max point on 4.

6. Jan 16, 2012

### Staff: Mentor

But you have a restricted domain, with x <= 0.

7. Jan 16, 2012

### FlopperJr

I believe the domain and range of the inverse is
x>4 and y≤0

Last edited: Jan 16, 2012
8. Jan 16, 2012

### Staff: Mentor

The domain of f is {x | x <= 0}
The range of f is what? You know what the graph of f looks like, so you should be able to answer that by looking at the graph.

Then look at what SammyS said in post #2 about the domain and range of f-1.

9. Jan 16, 2012

### FlopperJr

Okay thanks! I know that it is going to be oppsite of whatever the original function was.
Now that I see the graph, it would be x≤4.

10. Jan 16, 2012

### Staff: Mentor

That's better.

11. Jan 16, 2012

### FlopperJr

Thanks so much for your help!! I always have trouble with the domain and range.