Question

The function $f\left(x\right)=\frac{1}{x^4+x^2+1}$ is

• A. Discontinuous at $x=0$
• B. Discontinuous at $x=1$
• C. Discontinuous at $x=-1$
• D. Continuous at every where

Answer 1

The correct option is D Continuous at every where

$f\left(x\right)=\frac{1}{x^4+x^2+1}\Rightarrow f\left(x\right)=\frac{1}{{(x^2+\frac{1}{2})}^2+\frac{3}{4}}$
Now, ${(x^2+\frac{1}{2})}^2+\frac{3}{4}\ge 1\forall x\in R$
Hence, $f\left(x\right)$ is continuous $\forall x\in R$