Home
Class 12
MATHS
If composite function f1(f2(f3((fn(x))))...

If composite function `f_1(f_2(f_3((f_n(x))))n` timesis an decreasing function and if `'r'` functions out of total `'n'` functions are decreasing function while rest are increasing, then the maximum value of `r(n-r)` is (a) `(n^2-4)/4` , when `n` is of the form 4k (b) `(n^2)/4,` when `n` is an even number (c) `(n^2-1)/4,` when `n` is an odd number (d) `(n^2)/4,` when `n` is of the form 4k+2

Text Solution

AI Generated Solution

Promotional Banner

Similar Questions

Explore conceptually related problems

If f_(n) = {{:( (f_(n-1))/(2) " when " f_n-1 "is an even number"), (3* f_(n-1) + 1 " when " f_(n-1) " is an odd number "):} and f_(1) = 3 , then f_(5) =

The sum of the series 1+4+3+6+5+8+ upto n term when n is an even number (n^2+n)/4 2. (n^2+3n)/2 3. (n^2+1)/4 4. (n(n-1))/4 (n^2+3n)/4

If tanx=ntany ,n in R^+, then the maximum value of sec^2(x-y) is equal to (a) ((n+1)^2)/(2n) (b) ((n+1)^2)/n (c) ((n+1)^2)/2 (d) ((n+1)^2)/(4n)

If f:NrarrZ f(n)={(n-1)/2; when n is odd =-n/2; when n is even Identify the type of function

Let f: R-{n}->R be a function defined by f(x)=(x-m)/(x-n) such that m!=n 1) f is one one into function2) f is one one onto function3) f is many one into funciton4) f is many one onto function then

A function f:R to R is differernitable and satisfies the equation f((1)/(n)) =0 for all integers n ge 1 , then

A function f is defined such that f(1)=2, f(2)=5, and f(n)=f(n-1)-f(n-2) for all integer values of n greater than 2. What is the value of f(4)?

If f(n)=sum_(r=1)^(n) r^(4) , then the value of sum_(r=1)^(n) r(n-r)^(3) is equal to

The function f(x)=(4sin^2x−1)^n (x^2−x+1),n in N , has a local minimum at x=pi/6 . Then (a) n is any even number (b) n is an odd number (c) n is odd prime number (d) n is any natural number

Let f:R rarr R and f(x)=(3x^(2)+mx+n)/(x^(2)+1) . If the range of this function is [-4,3] , then the value of (m^(2)+n^(2))/(4) is ….