Question

Range of the function $f\left(x\right)=x^2+\frac{1}{x^2+1}$, is

• A. $[1,\infty )$
• B. $[2,\infty )$
• C. $[3,\infty )$
• D. $[0,\infty )$

Answer 1

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

for $f\left(x\right)$ to be existed $x^2+1>0$

but always $x^2>=0$

put $x=0$

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

this is the minimum value of $f\left(x\right)$

maximum value can be infinite

because $x^2>=0$

range is $[1,+\infty )$