Question

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

• A. $(1,+\infty )$
• B. $(2,+\infty )$
• C. $(\frac{3}{2}+\infty )$
• D. $noneofthese$

Answer 1

The correct option is A $(1,+\infty )$

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

Range of $x^2=[0,\infty )$

Range of $\frac{1}{x^2+1}=[0,1]$

Now, putting the value common in

above both,

Range of $f\left(x\right)=(1,\infty )$