Question

The domain of \(f(x) = \frac{x^2 + 1}{x^2 + x + 1}\) is

• A. $\mathbb{R}$
• B. $\mathbb{R} - \{2\}$
• C. $\mathbb{R} - \{1\}$
• D. $\mathbb{R} - \{0\}$
• E. $\mathbb{R} - \{1,-1\}$

Hint:

If quadratic denominator has negative discriminant, it is never zero for real $x$.

Answer 1

The Correct Option is A

Concept: Domain excludes values where denominator = 0.

Step 1: Check denominator
\[ x^2 + x + 1 = 0 \]

Step 2: Find discriminant
\[ D = 1 - 4 = -3 < 0 \]

Step 3: Conclusion
No real roots → denominator never zero Final Conclusion:
Domain = $\mathbb{R}$