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