(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello. My following problem is partially about the maths concept involved but is largely to do with what the question is actually asking? It's from an online quiz and a printscreen of it has been provided as an attachment.

2. Relevant equations

See attachments for the questions and a graph of one of the possible answers to help illustrate my point.

3. The attempt at a solution

Please look at the attachment with the graph (drawn in Paint sorry) of f(x) = [tex]\sqrt{x-3}[/tex] drawn in blue and its inverse in green. The question asks if it has an inverse for x > 1 but I'm not sure whether I'm looking at the domain of x > 1 for the inverse or the original function? f(x) has a domain of [3, [tex]\infty[/tex]) so I thought perhaps I would say 'no' to it as it isn't defined for all of x > 1. I then realised that the inverse function has a domain of [0, [tex]\infty[/tex]) so perhaps I should say yes as the inverse is defined for all of x > 1

This is my main query and it extends throughout the other 3 possible answers as well. I think I'm confidentially able to say 'yes' to (a) because both f(x) = ln(x+2) and its inverse are defined for x > 1 but that doesn't mean I fully understand what I'm being asked for.

Thank you kindly in advance for help on what I'm actually being asked for. Help on (b) would also be much appreciated because finding the inverse gets a bit harder when the inverse isn't actually defined as a function.

-David

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# Homework Help: Existence of Inverse Functions

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