For all real values of x, the expression x2−2x+4x2+2x+4 lies between 13 & 3. Then the values between which, the expression 9.32x+6.3x+49.32x−6.3x+4 lies, are

9.32x+6.3x+49.32x−6.3x+4=3x+12+2.3x+1+43x+12−2.3x+1+4,which clearly lies between 13 & 3.

For all real values of x, the expression x2−2x+4x2+2x+4 lies between 13 & 3. Then the values between which, the expression 9.32x+6.3x+49.32x−6.3x+4 lies, are

9.32x+6.3x+49.32x−6.3x+4=3x+12+2.3x+1+43x+12−2.3x+1+4,which clearly lies between 13 & 3.

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For all real values of $x$ , the expression $\frac{x^{2} - 2 x + 4}{x^{2} + 2 x + 4}$ lies between $\frac{1}{3} & 3$ . Then 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

$\frac{1}{3} & 3$

2 and 4

0 and 2

answer is C.

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$\frac{{9.3}^{2 x} + {6.3}^{x} + 4}{{9.3}^{2 x} - {6.3}^{x} + 4}$ $= \frac{{(3^{x + 1})}^{2} + {2.3}^{x + 1} + 4}{{(3^{x + 1})}^{2} - {2.3}^{x + 1} + 4},$ which clearly lies between $\frac{1}{3} & 3$ .

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For all real values of x, the expression x2−2x+4x2+2x+4 lies between 13 & 3. Then the values between which, the expression 9.32x+6.3x+49.32x−6.3x+4 lies, are

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For all real values of $x$ , the expression $\frac{x^{2} - 2 x + 4}{x^{2} + 2 x + 4}$ lies between $\frac{1}{3} & 3$ . Then 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