- Home
- Standard 12
- Mathematics
1.Relation and Function
normal
Let $f(x)=\frac{x+1}{x-1}$ for all $x \neq 1$. Let $f^1(x)=f(x), f^2(x)=f(f(x))$ and generally $f^n(x)=f\left(f^{n-1}(x)\right)$ for $n>1$. Let $P=f^1(2) f^2(3) f^3(4) f^4(5)$ Which of the following is a multiple of $P$ ?
A
$125$
B
$375$
C
$250$
D
$147$
(KVPY-2012)
Solution
(b)
We have, $f^1(x)=\frac{x+1}{x-1}$
$f^3(x) =f(x), f^4(x)=x$
$P =f^1(2) \cdot f^2(3) \cdot f^3(4) \cdot f^4(5)$
$P =3 \times 3 \times \frac{5}{3} \times 5=75$
$\therefore$ Multiple of $P$ is $375$
Standard 12
Mathematics
