Home
Class 12
MATHS
A=[(1,tan x),(-tan x,1)] and f(x) is def...

`A=[(1,tan x),(-tan x,1)]` and `f(x)` is defined as `f(x)=` det. `(A^(T)A^(-1))` then the value of `ubrace(f(f(f(f..........f(x)))))_("n times")` is `(n ge 2)`_______ .

Text Solution

Verified by Experts

The correct Answer is:
2
`because A = [[1,tan x],[-tan x,1]]`
`therefore det A + [[1, tan x],[-tan x, 1]]= (1+ tan^(2)x) = ""^(2)x`
`rArr det A^(T) = det A = sec^(2) x `
Now, `f(x) = det (A^(T) A^(-1)) = (det A^(T)) (detA^(-1))`
`= ( det A^(T) ) (det A)^(-1) = (det(A^(T)))/(detA)= 1 `
`therefore underset("n times")(underbrace(lambda = f(f(f(f...f(x))))))=1 [because f(x) = 1]`
Hence, `2^(lambda)= 2^(1) = 2`
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x)= x^(2)+x-1 then the value of f(1) is

If f:RtoR is defined by f(x)=x^(3) then f^(-1)(8)=

A function f is defined by f(x) = (2x-5) write the value of (i) f(7) (ii) f(-3) ?

f:R->R is defined as f(x)=2x+|x| then f(3x)-f(-x)-4x=

If f : R to R is defined by f(x) = x/(x^(2)+1) find f(f(2)) .

If function f:RtoR is defined by f(x)=3x-4 then f^(-1)(x) is given by

Let f: N rarr N be defined by f(x)=x^(2)+x+1 then f is

If f(x)= (1)/(1-x) , then f[f{x}]=

if f(x) = cos (log x) then the value of f(x) f(y)-(1//2) [f(x//y) + f(xy) ] is

If f : R to R is defined by f (x) = 2x + 3 , then f^(-1) x