Range and inverse of bijective functions

[MorallyObtuse]

Homework Statement

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)

 

[MorallyObtuse]

Anybody able to help?

 

[HallsofIvy]

Homework Statement

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)[/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?

 

[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 positive R.

 

[MorallyObtuse]

Someone able to help?