Question

The values of $b$ for which the function
$f\left(x\right)=\{\begin{array}{c}5x-4,0<x\le 1\\ 4x^2+3bx,1<x<2\end{array}$ is continuous at every point of its domain is

• A. $-1$
• B. $0$
• C. $1$
• D. $\frac{13}{3}$

Answer 1

Answer: (A)

$-1$

Given, $f\left(x\right)=\{\begin{array}{c}5x-4,0<x\le 1\\ 4x^2+3bx,1<x<2\end{array}$ is continuous at every point of its domain.

$f\left(x\right)$ is continuous.

$\Rightarrow L.H.L=R.H.L=f\left(1\right)$

$\Rightarrow {lim}_{x\to 1}5x-4={lim}_{x\to 1}4x^2+3bx=1$

$\Rightarrow 1=4+3b=1$
$\Rightarrow 3b=-3$
$\therefore b=-1$
Hence, option A.