The image is R, because f hasnīt restriction, you can draw the grafh and you will see that Im (f) = R
To find the inverse you must divide R in two intervalo, you must find de maximun or minimun, we say that this point is X, then:
I'm afraid Nacho is incorrect. He may be thinking of the "domain" rather than the "range" or image. Complete the square on that quadratic: . Now it should be clear that f(x) is never larger than 6. And that should make it clear how to solve for x to find the two "inverse" functions.
Ohh.. now it's a little bit clearer...
-How can I prove that f:R-->(inf,6] is not inverse?
-What are the two intervals that I must take to prove that f is inverse.
I mean: f_1-->(inf,6] and f_2-->(inf,6], which intervals should I take (D_1, D_2)?
And thank you a lot!