Given that- for all real - x- the expression 9-x2-2 x-4 x2-2 x-4 lies between 1-3 and 3 - The values between which the expression 9-32 x-6-3x-4-9-32 x-6-3x-4 lies are

The correct option is A 1/3 lt; x^2 2x+4/x^2+2x+4 lt; 3 for all xϵ R ⇒1/3 lt;x^2+2x+4/x^2 2x+4 lt;3 for all x ϵ R Let lt; 3^x+1=y, Then yϵ R for al ...

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Byju's Answer

Standard XII

Mathematics

Range

Given that, f...

Question

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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Solution

The correct option is A

$\frac{1}{3} < \frac{x^{2} - 2 x + 4}{x^{2} + 2 x + 4} < 3 f o r a l l x ϵ R \Rightarrow \frac{1}{3} < \frac{x^{2} + 2 x + 4}{x^{2} - 2 x + 4} < 3 f o r a l l x ϵ R$

$L e t < 3^{x + 1} = y, T h e n y ϵ R f o r a l l x ϵ R$

$F r o m (a) :: \frac{1}{3} < \frac{{9.3}^{2 x} + {6.3}^{x} + 4}{{9.3}^{2 x} - {6.3}^{x} + 4} < 3$

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Similar questions

Q. Given that, for all real

x,

the expression

\frac{x^{2} - 2 x + 4}{x^{2} + 2 x + 4}

lies between

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. The values between which the expression

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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