Question

Can anyone help me out on this question?

Answer 1

Firstly , we will check continuity at x=1

we can use method

Suppose, f(x) is continuous at x=c

then it must satisfy

$\lim_{x \to c} f(x)=f(c)$

$\lim_{x \to 1} f(x)=f(1)$

firstly , we can find limit

$\lim_{x \to 1-} f(x)= \lim_{x \to 1-}(x+3)=1+3=4$

$\lim_{x \to 1+} f(x)= \lim_{x \to 1-}(3x+1)=3*1+1=4$

so, we get

$\lim_{x \to 1} f(x)= 4$

now, we can find f(1)

$f(1)=3*1+1=4$

so, we got

$\lim_{x \to 1} f(x)=f(1) =4$

so, this is continuous at x=1

Hence , option-D...........................Answer