Question

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

• A. $[1,\infty )$
• B. $[2,\infty )$
• C. $[\frac{3}{2},\infty )$
• D. None

Answer 1

The correct option is A $[1,\infty )$

$f\left(x\right)=x^2+\frac{1}{x^2+1}$

When $x=0$

$f\left(x\right)=x^2+\frac{1}{x^2+1}$

$=0+\frac{1}{0+1}$

$=1$

When $x>0$

$f\left(x\right)>1$

When $x<0$

$f\left(x\right)>1$

So the range of $f\left(x\right)=[1,\infty )$