# Finding the number of continuous inverses for a function [closed]

$$f(x)=x^3+3x$$ Question asks me to find the number of continuous inverses of the function. So first of all I didn't get what is meant by "number of continuous inverses of the function" I mean if a function is continuous on all it's domain I can define an interval $[a- \epsilon,b - \epsilon]$ And since interval is compact by compact graph theory $g=f^-1$ the inverse of f, will be continuous for $\forall \epsilon>0$ Therefore infinite number of continuous inverses exist.

Or as the number of continuous inverses, did they mean how many functions have the reflection of the graph of $f$ around $y=x$ as it's graph?

I couldn't understand what is meant by this, anyway .

Looking at $f'(x)=3x^2+3$ We see that $f'(x)>0$ ==> $f$ is strictly increasing.

Then we can find a $g$ since $f$ is strictly increasing implies $f$ is monotonic.

But how would I show that $g$ is continuous

## closed as off-topic by Adam Hughes, E. Joseph, астон вілла олоф мэллбэрг, Daniel W. Farlow, John BDec 4 '16 at 1:03

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Adam Hughes, E. Joseph, астон вілла олоф мэллбэрг, Daniel W. Farlow, John B
If this question can be reworded to fit the rules in the help center, please edit the question.