Question

The range of the function f(x)=x²-x+1x²+x+1, where xR, is:

• A. (-∞,3]
• B. (-∞,∞)
• C. [3,∞)
• D. [\frac13,3]

Hint:

Use discriminant condition to find range.

Answer 1

The Correct Option is D

Let y=x²-x+1x²+x+1. y(x²+x+1)=x²-x+1 (y-1)x²+(y+1)x+(y-1)=0 For real x, discriminant \ge0: (y+1)²-4(y-1)²\ge0 3y²-10y+3\le0 (y-3)(3y-1)\le0 \frac13 y\le3