Question

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

A
1
B
0
C
1
D
133

Solution

## The correct option is B $$-1$$Given, $$f(x)=\begin{cases} 5x-4,\quad 0<x\le 1 \\ 4{ x }^{ 2 }+3bx,\quad 1<x<2 \end{cases}$$ is continuous at every point of its domain.$$f(x)$$ is continuous.$$\Rightarrow L.H.L=R.H.L=f(1)\\$$$$\Rightarrow \lim _{ x\rightarrow 1 }{ \quad 5x-4 } =\lim _{ x\rightarrow 1 }{ \quad 4{ x }^{ 2 }+3bx } = 1\\$$$$\Rightarrow 1=4+3b=1\\$$$$\Rightarrow 3b=-3\\$$$$\therefore b=-1\\$$Hence, option A.Mathematics

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