If $f$ is an even function defined on the interval $(-5, 5)$, then four real values of $x$ satisfying the equation $f(x) = f\left( {\frac{{x + 1}}{{x + 2}}} \right)$ are
If $f$ is an even function defined on the interval $(-5, 5)$, then four real values of $x$ satisfying the equation $f(x) = f\left( {\frac{{x + 1}}{{x + 2}}} \right)$ are
- A
$\frac{{ - 3 - \sqrt 5 }}{2},\frac{{ - 3 + \sqrt 5 }}{2},\frac{{3 - \sqrt 5 }}{2},\frac{{3 + \sqrt 5 }}{2}$
- B
$\frac{{ - 5 + \sqrt 3 }}{2},\frac{{ - 3 + \sqrt 5 }}{2},\frac{{3 + \sqrt 5 }}{2},\frac{{3 - \sqrt 5 }}{2}$
- C
$\frac{{3 - \sqrt 5 }}{2},\frac{{3 + \sqrt 5 }}{2},\frac{{ - 3 - \sqrt 5 }}{2},\frac{{5 + \sqrt 3 }}{2}$
- D
$ - 3 - \sqrt 5 , - 3 + \sqrt 5 ,3 - \sqrt 5 ,3 + \sqrt 5$
Similar Questions
Consider the function $\mathrm{f}:\left[\frac{1}{2}, 1\right] \rightarrow \mathrm{R}$ defined by $f(x)=4 \sqrt{2} x^3-3 \sqrt{2} x-1$. Consider the statements
$(I)$ The curve $y=f(x)$ intersects the $x$-axis exactly at one point
$(II)$ The curve $y=f(x)$ intersects the $x$-axis at $\mathrm{x}=\cos \frac{\pi}{12}$
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$(I)$ The curve $y=f(x)$ intersects the $x$-axis exactly at one point
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Then
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$R _{1}=\left\{( a , b ) \in R ^{2}: a ^{2}+ b ^{2} \in Q \right\}$ and $R _{2}=\left\{( a , b ) \in R ^{2}: a ^{2}+ b ^{2} \notin Q \right\}$
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