answersLogoWhite

0

If a function is even ie if f(-x) = f(x). Such a function would be symmetric about the y-axis. So f(x) is a many-to-one function. The inverse mapping then is one-to-many which is not a function.

In fact, the function need not be symmetric about the y-axis. Symmetry about x=k (for any constant k) would also do.

Also, leaving aside the question of symmetry, the existence of an inverse depends on the domain over which the original function is defined. Thus, y = f(x) = x2 does not have an inverse if f is defined from the real numbers (R) to R. But if it is defined from (and to) the non-negative Reals there is an inverse - the square-root function.

User Avatar

Wiki User

14y ago

Still curious? Ask our experts.

Chat with our AI personalities

JordanJordan
Looking for a career mentor? I've seen my fair share of shake-ups.
Chat with Jordan
MaxineMaxine
I respect you enough to keep it real.
Chat with Maxine
RossRoss
Every question is just a happy little opportunity.
Chat with Ross

Add your answer:

Earn +20 pts
Q: What kind of symmetry indicates that a function will not have an inverse?
Write your answer...
Submit
Still have questions?
magnify glass
imp