Question

Let $f:R\to R$ be a function such that $f\left(x\right)=x^3-6x^2+11x-6$, then $f\left(x\right)$ is

• A. one-one onto
• B. one-one into
• C. many one onto
• D. many one into

Answer 1

Answer: (C)

many one onto

Since f is third order polynomial $\Rightarrow$Range of f is $R$

Hence f is onto function.
Now, $f^{\prime }\left(x\right)=3x^2-12x+11$

Discriminant of above quadratic is $={12}^2-12\times 11=12>0$

Hence f is not monotonic function $\Rightarrow$ f is many one function