AP EAMCET · Maths · Functions
For real value of \(x\), the range of \(\frac{x^2+2 x+1}{x^2+2 x-1}\) is
- A \((-\infty, 0) \cup(1, \infty)\)
- B \(\left[\frac{1}{2}, 2\right]\)
- C \(\left(-\infty, \frac{-2}{9}\right] \cup(1, \infty)\)
- D None of these
Answer & Solution
Correct Answer
(D) None of these
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Let } y=\frac{x^2+2 x+1}{x^2+2 x-1} \\ & y\left(x^2+2 x-1\right)=x^2+2 x+1 \\ & y x^2+2 x y-y=x^2+2 x+1 \\ & y x^2-x^2+2 x y-2 x-y-1=0 \\ & (y-1) x^2+2(y-1) x-y-1=0 \end{aligned}\) For real values of \(x, b^2-4 a c \geq 0\)…
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