Pre-calculus question

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Pre-calculus question

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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its B...
replace f(x) by y and x by f inverse x.... and then solve.. you will get option B

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Other answers:

A function must have exactly one "y value" for a given "x value". Look at the options, all of them are of form \(y=\pm \text{somthing}\), which means, the \(y\) values are not unique. What can you infer fromm this ?
It is not a function, because there are more than one y value?
Exactly!
see when a function has a non zero derivative at a point then it is invertible in the neighbourhood
Answer is either A or C
and if it would not be a function then how can you calculate inverse of it..
i think it is a function. and answer should be B.
good question, looks they don't care about these fine details at school level
Well I'm pretty sure the answer is C...
so avoiding any complexity to the best of the data provided the answer should be B for sure
I bet my 10 cents on A or C
ribhu, I think it is C.
Ok, thanks for your help!! @ganeshie8 and @ribhu
I think, we may say the inverse of given function is a multivalued function. But, we cannot say the inverse is a function... @ribhu please enlighten me as you seem to have good real analysis knowledge :)

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