Question

Let f(x) = x + 1; where $xϵ[0,\infty ]$. Choose the right option.

• A. f(x) is continuous at
• B. f(x) is discontinuous at
• C. f(x) is discontinuous at but removable
• D. None of these

Answer 1

The correct option is A

f(x) is continuous at

Here the function is defined in the domain $[0,\infty )$. i.e., if we are checking for discontinuity at the point $x=0$, there is no need to find the left hand limit of $x=0$, this is because the function is not defined at all to the left of $x=0$.

So in this case f(x) is continuous at $x=0$,

$=f\left(0\right)$

i.e., $=f\left(0\right)$

$=0+1$

$L=1$

$\therefore$ function is continuous at $x=0$