Question

The set of points of discontinuity of the$f\left(x\right)=\frac{1}{x^2+x+1}$

• A. $\varphi$
• B. $R$
• C. $\left\{0\right\}$
• D. $R^{-}$

Answer 1

The correct option is A $\varphi$

The given function will be discontinuous at all those points where it is not defined.
Thus, for this the denominator should not be equal to 0
For $x^2+x+1$, we see that it is always gretaer than $\frac{3}{4}$, as
${(x+\frac{1}{4})}^2+\frac{3}{4}$ = $x^2+x+1$
Hence, the function is continuous for all x lying along the number line