Inverse Function Help: given g(x)= x^2+x+1, evaluate g(g^(-1)(x))

[shaash]

Here is the problem I was faced with:
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g(x)= x²+x+1
evaluate g(g^-1(x))
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So I know that one way to solve this would be to find the inverse of g(x) and plug in whatever I get in to g(x).
However, my teacher told me that if you plug in the inverse of a function in to the original function, the answer is X.
This is what is happening in this case, so I believe the answer is X. However, some of my peers told me that in the
case of this specific problem, that is not true. They claim that since the inverse of g(x) is not a function, this rule does
not apply.
My question is am I right, or are my friends?


Btw the rule that my math teacher taught me can be expressed as:
f(f-1(x))=x


This looks awfully similar to the problem I was asked to solve. However, my teacher wasn't specific if the above equation
is true in all scenarios, or only if f-1(x) is a function.


Thanks in advance. By the way, I would really really really REALLY appreciate a prompt reply, even if you aren't 100% sure.
My test is TOMORROW! :sad:

 

[stapel]

As you know (from the Horizontal Line Test), this function is not invertible; its inverse is not itself a function. So, unless you've been given a restricted domain, either there is no answer or else you need to do this piecewise (depending upon your book and instructor, probably).