Question

A function f(x) is defined as

$f\left(x\right)=\{\begin{array}{cc}3x+4& x<0\\ -4& x=0\\ 4-6x& x>0\end{array}$

then at x = 0 for f(x)

• A. Limit does not exists
• B. Limit exists but discontinous
• C. Limit exists and is continuous
• D. Is not defined

Answer 1

The correct option is B Limit exists but discontinous

For limit to exist, LHL = RHL

Now,

RHL $li{m}_{x\to 0^{+}}f\left(x\right)=4-6x=4$

LHL $li{m}_{x\to 0^{-}}f\left(x\right)=3x+4=4$

$\Rightarrow$ Limit exists

Now for continuity,

LHL = RHL = Functional value
At x = 0
$f\left(x\right)=-4\ne RHL$

$\Rightarrow$ Discontinous