Inverse function - domain

• Mar 28th 2010, 11:59 PM
xwrathbringerx
Inverse function - domain
Hi

State a domain for which the function y = (x-1)^2-3 does not have an inverse. Give a brief reason for your answer.

Could someone please explain the solution to me: The function will not have an inverse if there are included values of x on both sides of x=1, so no inverse for -1<= x <=3, say.

I've found the inverse function: y = 1+sqrt[x+3]
• Mar 29th 2010, 12:06 AM
sa-ri-ga-ma
Quote:

Originally Posted by xwrathbringerx
Hi

State a domain for which the function y = (x-1)^2-3 does not have an inverse. Give a brief reason for your answer.

Could someone please explain the solution to me: The function will not have an inverse if there are included values of x on both sides of x=1, so no inverse for -1<= x <=3, say.
I've found the inverse function: y = 1+sqrt[x+3]

Square root of negative quantity is not possible. In the given problem at what value of x it happens?
• Mar 29th 2010, 12:06 AM
mr fantastic
Quote:

Originally Posted by xwrathbringerx
Hi

State a domain for which the function y = (x-1)^2-3 does not have an inverse. Give a brief reason for your answer.

Could someone please explain the solution to me: The function will not have an inverse if there are included values of x on both sides of x=1, so no inverse for -1<= x <=3, say.

I've found the inverse function: y = 1+sqrt[x+3]

Does not have an inverse function, I assume you mean. Answer: Any domain over which the given function is NOT one-to-one.

Quote:

Originally Posted by sa-ri-ga-ma
Square root of negative quantity is not possible. In the given problem at what value of x it happens?

Since the domain of the inverse function is equal to the range of the function, this is not a relevant question to ask.