If the function f(x) = , * 20 c 5x - 4 &,& if & 0 < x 1 4 x^2 + 3… - Vidyadip

MCQ

If the function $f(x) = \,\left\{ {\begin{array}{*{20}{c}}{5x - 4}&,&{{\rm{if}}}&{0 < x \le 1}\\{4{x^2} + 3bx}&,&{{\rm{if}}}&{1 < x < 2}\end{array}} \right.$ is continuous at every point of its domain, then the value of $b$ is

✓
$-1$
B
$0$
C
$1$
D
None of these

✓

Answer

Correct option: A.

$-1$

a
(a) $f(x)$ is continuous at every point of its domain,

==>$\mathop {\lim }\limits_{x \to {1^ - }} f(x) = \mathop {\lim }\limits_{x \to {1^ + }} f(x) = f(1)$

==> $5 \times 1 - 4 = 4 \times 1 + 3 \times b \times 1$

==> $1 = 4 + 3b$ ==> $3b = - 3$ ==> $b = - 1$.

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