Range and inverse of bijective functions

AI Thread Summary
For the bijective function f(x) = x² - 1 with x ≥ 0, the correct range is [−1, ∞) rather than (0, ∞), as f(0) equals -1. The inverse function is found to be x = √(y + 1), but its domain must also be specified. For the second function f(x) = (x + 1)² with x ≤ -2, the range is [0, ∞) since the minimum output occurs at x = -2. Understanding the definitions of range and domain is crucial for solving these problems accurately.
MorallyObtuse
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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)
 
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Anybody able to help?
 
MorallyObtuse said:

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?
 
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.
 
Someone able to help?
 

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