# Range and inverse of bijective functions

1. Nov 15, 2009

### MorallyObtuse

1. The problem statement, all variables and given/known data
For each of the following bijective functions find the range S and the inverse:

a.) f : x |→ x² - 1 (x ∈ R, x ≥ 0)

b.) f : x |→ (x + 1)² ((x ∈ R, x ≤ -2)........Not sure how to do this one, help please

2. The attempt at a solution

a.) http://hotmath.com/images/gt/lessons/genericalg1/parabola.gif
the range (S) for the graph is (0,∞)
Inverse = x² - 1
x = √(y + 1)

2. Nov 16, 2009

### MorallyObtuse

Anybody able to help?

3. Nov 16, 2009

### HallsofIvy

Staff Emeritus
2. The attempt at a solution

a.) http://hotmath.com/images/gt/lessons/genericalg1/parabola.gif
the range (S) for the graph is (0,∞)
Inverse = x² - 1
x = √(y + 1)[/QUOTE]
a) No, the range is NOT (0,∞). Are you clear on what range is? What is f(0)? Your graph is for y= x2, not y= x2- 1.

And you haven't completely described the inverse until you have told what its domain is.

b) x+1 is just x, "shifted over 1". Do you know what the range of x2 is?

4. Nov 16, 2009

### MorallyObtuse

The range is the set of output numbers of a function. f(0) would be -1
The domain is the set of inputs for a function.

The range of x2 is 0 or and postive R.

5. Nov 16, 2009

### MorallyObtuse

Someone able to help?