## vera_ewing one year ago Pre-calculus question

1. vera_ewing

2. ribhu

its B...

3. ribhu

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

4. ganeshie8

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 ?

5. vera_ewing

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

6. ganeshie8

Exactly!

7. ribhu

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

8. ganeshie8

Answer is either A or C

9. ribhu

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

10. ribhu

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

11. ganeshie8

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

12. vera_ewing

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

13. ribhu

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

14. ganeshie8

I bet my 10 cents on A or C

15. vera_ewing

ribhu, I think it is C.

16. vera_ewing

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

17. ganeshie8

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 :)