Pre-calculus question

Question

vera_ewing · Answer

attachment

ribhu · Answer

its B...

ribhu · Answer

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

ganeshie8 · Answer

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 ?

vera_ewing · Answer

It is not a function, because there are more than one y value?

ganeshie8 · Answer

Exactly!

ribhu · Answer

see when a function has a non zero derivative at a point then it is invertible in the neighbourhood

ganeshie8 · Answer

Answer is either A or C

ribhu · Answer

and if it would not be a function then how can you calculate inverse of it..

ribhu · Answer

i think it is a function. and answer should be B.

ganeshie8 · Answer

good question, looks they don't care about these fine details at school level

vera_ewing · Answer

Well I'm pretty sure the answer is C...

ribhu · Answer

so avoiding any complexity to the best of the data provided the answer should be B for sure

ganeshie8 · Answer

I bet my 10 cents on A or C

vera_ewing · Answer

ribhu, I think it is C.

vera_ewing · Answer

Ok, thanks for your help!! @ganeshie8 and @ribhu

ganeshie8 · Answer

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 :)