Answer to Question #235125 in Discrete Mathematics for mickey

Question

Determine whether each of these functions is a bijection from R to R.

f (x) = (x2 + 1)/(x2 + 2)

Answer 1

$f(x) = \frac{x^2+1}{x^2+2} \\ For \; x=-1 => f(x) = \frac{1+1}{1+2}= \frac{2}{3} \\ For\; x=1 => f(x) = \frac{1+1}{1+2}= \frac{2}{3}$

=> Not one-to-one function

=> Not a bijective (no inverse exists)