Question

Classify the following functions $f(x)$ defined in $R \rightarrow R$ as injective, surjective, both or none.

(i) $f(x)=\frac{x^2}{1+x^2}$

(ii) $f(x)=x^3-6 x^2+11 x-6$

Answer 1

(i) $f(x)=\frac{x^2}{1+x^2} \quad$ even function $\Rightarrow$ many one $1>f(x) \geq 0 \quad$ into function

(ii) $f(x)=x^3-6 x^2+11 x-6 \\$ 

$f(x)=(x-1)(x-2)(x-3)$

many one onto function