Question

Let $f:R\to R$ be defined by $f\left(x\right)=\{\begin{array}{c}k-2x,ifx\le -1\\ 2x+3,ifx>-1\end{array}$ be continous. then find possible value of $k$ is

• A. $0$
• B. $-\frac{1}{2}$
• C. $-1$
• D. $1$

Answer 1

Answer: (C)

$-1$

$f\left(x\right)=k-2x$ if $x\le -1$

$=2x+3$ if $x>-1$

So, $L.H.L.=R.H.L.$

$k-2x=2x+3$

$k=4x+3$

For $x=-1$, $k=-1$

Hence, option ${}^{\prime }{C}^{\prime }$ is correct.