Answer
not continuous
Work Step by Step
$f(x)$ will be continuous at $x=1$ if $f(1)=\lim_{x\to 1}f(x)$. We know that $f(1)=2$.
$$\lim_{x\to 1^+}f(x)\\=\lim_{x\to 1^+}\frac{3}{x+1}\\=\lim_{x\to 1^+}\frac{3}{1+1}\\=\frac{3}{2}$$
$\frac{3}{2}\ne2$, hence it is not continuous at $1$.
