AP EAMCET · Maths · Functions
The range of the function \(f(x)=\frac{x^2+x+1}{x^2-x+1}\) is
- A \(\left[\frac{1}{3}, 3\right]\)
- B \(\left[\frac{1}{2}, 2\right]\)
- C \(\left[\frac{-1}{2}, \frac{-1}{4}\right]\)
- D \(\left[\frac{-1}{2}, 2\right]\)
Answer & Solution
Correct Answer
(A) \(\left[\frac{1}{3}, 3\right]\)
Step-by-step Solution
Detailed explanation
Let \(y=\frac{x^2+x+1}{x^2-x+1}\) \(\begin{aligned} & \Rightarrow y x^2-x y+y=x^2+x+1 \\ & \Rightarrow \quad(y-1) x^2-(y+1) x+(y-1)=0\end{aligned}\) For real \(x\), \(D \geq 0\)…
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