The range of the function $f(x)=x^2+\frac{1}{x^2+1}$ is
Answer & explanation
Correct answer: option 1
$f(x)=x^2+\frac{1}{1+x^2}$
as $x=0$ $f(x)=1$
$x > 0$ or $x < 0 ⇒ x^2 > 0 ⇒ f(x) > 1$
so $f(x) ≥ 1$
The range of the function $f(x)=x^2+\frac{1}{x^2+1}$ is
Correct answer: option 1
$f(x)=x^2+\frac{1}{1+x^2}$
as $x=0$ $f(x)=1$
$x > 0$ or $x < 0 ⇒ x^2 > 0 ⇒ f(x) > 1$
so $f(x) ≥ 1$