Let $f:\mathbb{R}\rightarrow \mathbb{R}$ be a function defined as $f(x)=x+1$. Then $f$ is\\

Continuous at every point Discontinuous at $x=1$ Discontinuous at $x=-1$ None of the above

Continuous at every point

Let $a$ be any point in $\mathbb{R}$. We have $\lim_{x \to a}f(x)=a+1=f(a)$. Hence $f$ is continuous at $a$. Since $a$ is an arbitrary point, $f$ is continuous at every point on the domain.