Answer to Question #234691 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-one function

=> Not a bijective (no inverse exists)