Question

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

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

Answer 1

Answer: (A)

$\left[1\infty \right)$

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

Since $x^2\ge 0$.

Now, $x^2\ge 0,f\left(x\right)\ge 1$ or $f\left(x\right)\in [1,\infty )$.