Maths. Section AContinuity and Differentiability

Let f:ℝ→ ℝ be a function defined as f(x)=x+1. Then f is

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

Answer & explanation

Correct answer: option 1

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.