Question

If the function $f\left(x\right)=\{\begin{array}{cc}2x^2-3& \text{if}0<x\le 1\\ x^2+bx-1& \text{if}1<x<2\end{array}$ is continuous at every point of its domain then the value of $b$ is

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is A $-1$

$f\left(x\right)=\{\begin{array}{cc}2x^2-3& \text{if}0<x\le 1\\ x^2+bx-1& \text{if}1<x<2\end{array}$

$\because f\left(x\right)$ is continuous at $x=1$.

$\Rightarrow f(1-)=f(1+)=f\left(1\right)$

$\Rightarrow 2-3=1+b-1$

$\Rightarrow b=-1$