Solution to Determine whether each of these functions is a bijection from R to R?f (x) = … - Sikademy
Author Image

Archangel Macsika

Determine whether each of these functions is a bijection from R to R?f (x) = (x2 + 1)/(x2 + 2)

The Answer to the Question
is below this banner.

Can't find a solution anywhere?

NEED A FAST ANSWER TO ANY QUESTION OR ASSIGNMENT?

Get the Answers Now!

You will get a detailed answer to your question or assignment in the shortest time possible.

Here's the Solution to this Question

Let us determine whether the function f:\R \to \R,\ f (x) = \frac{x^2 + 1}{x^2 + 2}, is a bijection. Taking into account that for x_1=-1 and x_2=1\ne x_1 we get

f(x_1)=f(-1)= \frac{(-1)^2 + 1}{(-1)^2 + 2}=\frac{2}{3}=\frac{1^2 + 1}{1^2 + 2}=f(1)=f(x_2),

we conclude that the function f is not an injection, and hence this function is not a bijection.


Related Answers

Was this answer helpful?

Join our Community to stay in the know

Get updates for similar and other helpful Answers

Question ID: mtid-5-stid-8-sqid-2643-qpid-1113