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
- [IIT 1996]
- 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
Let $A=\{1,2,3,5,8,9\}$. Then the number of possible functions $f : A \rightarrow A$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to $...............$.
Let $A=\{1,2,3,5,8,9\}$. Then the number of possible functions $f : A \rightarrow A$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to $...............$.
- [JEE MAIN 2023]
The graph of the function $f(x)=x+\frac{1}{8} \sin (2 \pi x), 0 \leq x \leq 1$ is shown below. Define $f_1(x)=f(x), f_{n+1}(x)=f\left(f_n(x)\right)$, for $n \geq 1$.
Which of the following statements are true?
$I.$ There are infinitely many $x \in[0,1]$ for which $\lim _{n \rightarrow \infty} f_n(x)=0$
$II.$ There are infinitely many $x \in[0,1]$ for which $\lim _{n \rightarrow \infty} f_n(x)=\frac{1}{2}$
$III.$ There are infinitely many $x \in[0,1]$ for which $\lim _{n \rightarrow \infty} f_n(x)=1$
$IV.$ There are infinitely many $x \in[0,1]$ for which $\lim _{n \rightarrow \infty} f_n(x)$ does not exist.
The graph of the function $f(x)=x+\frac{1}{8} \sin (2 \pi x), 0 \leq x \leq 1$ is shown below. Define $f_1(x)=f(x), f_{n+1}(x)=f\left(f_n(x)\right)$, for $n \geq 1$.
Which of the following statements are true?
$I.$ There are infinitely many $x \in[0,1]$ for which $\lim _{n \rightarrow \infty} f_n(x)=0$
$II.$ There are infinitely many $x \in[0,1]$ for which $\lim _{n \rightarrow \infty} f_n(x)=\frac{1}{2}$
$III.$ There are infinitely many $x \in[0,1]$ for which $\lim _{n \rightarrow \infty} f_n(x)=1$
$IV.$ There are infinitely many $x \in[0,1]$ for which $\lim _{n \rightarrow \infty} f_n(x)$ does not exist.
- [KVPY 2016]
The domain of definition of the function $y(x)$ given by ${2^x} + {2^y} = 2$ is
The domain of definition of the function $y(x)$ given by ${2^x} + {2^y} = 2$ is
- [IIT 2000]
Minimum integral value of $\alpha$ for which graph of $f(x) = ||x -2| -\alpha|-5$ has exactly four $x-$intercepts-
Minimum integral value of $\alpha$ for which graph of $f(x) = ||x -2| -\alpha|-5$ has exactly four $x-$intercepts-
The range of values of the function $f\left( x \right) = \frac{1}{{2 - 3\sin x}}$ is
The range of values of the function $f\left( x \right) = \frac{1}{{2 - 3\sin x}}$ is