Range and inverse of bijective functions

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Homework Help Overview

The discussion revolves around finding the range and inverse of specific bijective functions, particularly focusing on the functions f(x) = x² - 1 for x ≥ 0 and f(x) = (x + 1)² for x ≤ -2. Participants are exploring the properties of these functions and clarifying the definitions of range and inverse.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to identify the range and inverse of the given functions but expresses uncertainty, particularly with the second function. Some participants question the accuracy of the range identified for the first function and seek clarification on the definition of range and how it applies to the functions in question.

Discussion Status

Participants are actively engaging with the problem, with some providing insights into the definitions of range and domain. There is a recognition of differing interpretations regarding the range of the first function, and guidance is being offered to clarify these concepts without reaching a consensus.

Contextual Notes

There is a mention of specific constraints regarding the domains of the functions being discussed, which may affect the determination of their ranges and inverses. The original poster's confusion about the second function indicates a need for further exploration of its properties.

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 positive R.
 
Someone able to help?
 

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