The value of a for which the function f(x)= 5x-4,&if 0 < x 1 4x^2… - Vidyadip

MCQ

The value of a for which the function $\text{f(x)}=\begin{cases}5\text{x}-4,&\text{if }0 < \text{x}\leq1\\4\text{x}^2+3\text{ax},&\text{if } < \text{x} < 2\end{cases}$ is continuous at every point of its domain, is :

A
$\frac{13}{3}$
B
$1$
C
$0$
✓
$-1$

✓

Answer

Correct option: D.

$-1$

$\lim\limits_{\text{x}\rightarrow1^-}\text{f(x)}=\lim\limits_{\text{x}\rightarrow1^+}\text{f(x)}$
$\lim\limits_{\text{x}\rightarrow1}5\text{x}-4=\lim\limits_{\text{x}\rightarrow1}4\text{x}^2+3\text{ax}$
$1=4+3\text{a}$
$\text{a}=-1$

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