question_answer

Let \[f(x)=\left\{ \begin{matrix}    x+1; & x<1  \\    \lambda ; & x=1  \\    {{x}^{2}}-x+3; & x>1  \\ \end{matrix} \right.\] be a strictly increasing function at \[x=1\], then the set of values of \['\lambda '\] are

A)  (2, 3)                                    

B)  [2, 3)

C)  [2, 3]                                    

D)  \[\phi \]

Correct Answer: C

Solution :

\[\Rightarrow \]\[2\le \lambda \le 3\]