Prove that the function $$f:\Bbb R\setminus\{1\} \to\Bbb R\ \ f(x)= \frac{x^2}{x-1}$$ is neither injective nor subjective.
For the function to be non-injective I have to disprove that $$f(x_1)=f(x_2)\implies x_1=x_2 \ \ or\ x_1\neq x_2\implies f(x_1)\neq f(x_2).$$
For $f(x)$ to be non surjective I have to find at leat one image that is not hit by a pre-image.
Can someone help me find these values and/or show how it is done properly?
Thank you!
Best Answer
$f(-1)=f(\frac{1}{2})$ so $f$ is not injective
and $f(x)=2$ has no solution so $f$ is not surjective