Given that, for all real x, the expression x2-2x+4x2+2x+4 lies between 13 and 3. The values between which the expression 9.32x+6.3x+49.32x-6.3x+4lies are

Let y= x2−2x+4x2+2x+4∴ 13<y<y∴ 9.32x+6.3x+49.32x−6.3x+4= (−3.3x)2−2(−3.3x)+4(−3.3x)2+2(−3.3x)+4Let −3.3x=a then= a2−2a+4a2+2a+4= y

Given that, for all real x, the expression x2-2x+4x2+2x+4 lies between 13 and 3. The values between which the expression 9.32x+6.3x+49.32x-6.3x+4lies are

Let y= x2−2x+4x2+2x+4∴ 13<y<y∴ 9.32x+6.3x+49.32x−6.3x+4= (−3.3x)2−2(−3.3x)+4(−3.3x)2+2(−3.3x)+4Let −3.3x=a then= a2−2a+4a2+2a+4= y

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Given that, for all real x, the expression $\frac{x^{2} - 2 x + 4}{x^{2} + 2 x + 4}$ lies between $\frac{1}{3}$ and 3. The values between which the expression $\frac{9 . 3^{2 x} + 6 . 3^{x} + 4}{9 . 3^{2 x} - 6 . 3^{x} + 4}$ lies are

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–1 and 1

0 and 2

1/3 and 3

–2 and 0

answer is A.

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Detailed Solution

$\begin{array}{l} L e t y = \frac{x^{2} - 2 x + 4}{x^{2} + 2 x + 4} \\ ∴ \frac{1}{3} < y < y \\ ∴ \frac{{9.3}^{2 x} + {6.3}^{x} + 4}{{9.3}^{2 x} - {6.3}^{x} + 4} = \frac{{(- {3.3}^{x})}^{2} - 2 (- {3.3}^{x}) + 4}{{(- {3.3}^{x})}^{2} + 2 (- {3.3}^{x}) + 4} \\ L e t - {3.3}^{x} = a t h e n \\ = \frac{a^{2} - 2 a + 4}{a^{2} + 2 a + 4} = y \end{array}$