Question

Let $f\left(x\right)=\{\begin{array}{c}x+1;x<1\\ \lambda ;x=1\\ x^2-x+3;x>1\end{array}$ 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. $\varphi$

Answer 1

Answer: (C)

$[2,3]$

$f\left(x\right)=$

$x+1;x<1$

$\lambda ;x=1$

$x^2-x+3;x>1$

$\text{since, at}x<1$

$f\left(x\right)=(-\infty ,2)$

and

at $x>1$

$f\left(x\right)=(3,\infty )$

$\text{For}f\left(x\right)\text{to be strictly increasing}$

So, $\lambda$ must be [2,3]