The range of the function $f(x)=x^2+\frac{1}{x^2+1}$ is

$[1, \infty)$ $[2, \infty)$ $\left.\frac{3}{2}, \infty\right)$ None of these

$[1, \infty)$

$f(x)=x^2+\frac{1}{1+x^2}$ as $x=0$  $f(x)=1$ $x > 0$ or $x < 0 ⇒ x^2 > 0 ⇒ f(x) > 1$ so $f(x) ≥ 1$