Home
Class 12
MATHS
If f is a bijection satisfying f'(x)=sqr...

If f is a bijection satisfying `f'(x)=sqrt((1-{f(x)}^(2))`, then `(f^(1))'x`

Text Solution

Verified by Experts

The correct Answer is:
2
`int_(0)^(1)(f(x).x(f(x))^(2))dx=int_(0)^(1) (x^(2))/4 dx`
`int_(0)^(1)[(f(x))^(2)-x.f(x)+(x^(2))/4]dx=0`
`int_(0)^(1)(f(x)-x/2)^(2) dx=0`
`impliesf(x)=x/2`
`:.f^(')(x)=1/2`
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x)=sqrt(x^(2)-2x+1), then f' (x) ?

Let f be a one-one function satisfying f'(x)=f(x) then (f^-1)''(x) is equal to

If f' is a differentiable function satisfying f(x)=int_(0)^(x)sqrt(1-f^(2)(t))dt+1/2 then the value of f(pi) is equal to

If f(x)=sqrt(1-sin2x), then f'(x) equals

If f(x) is a function satisfying f(x)-f(y)=(y^y)/(x^x)f((x^x)/(y^y))AAx , y in R^*"and"f^(prime)(1)=1 , then find f(x)

If a function satisfies f(x+1)+f(x-1)=sqrt(2)f(x) , then period of f(x) can be

If f(x)=(x-4)/(2sqrt(x)) , then find f'(1)

Statement -1: Let f(x) be a function satisfying f(x-1)+f(x+1)=sqrt(2)f(x) for all x in R . Then f(x) is periodic with period 8. Statement-2: For every natural number n there exists a periodic functions with period n.

Let g(x) be a polynomial of degree one and f(x) be defined by f(x)=-g(x), x 0 If f(x) is continuous satisfying f'(1)=f(-1) , then g(x) is

If a function 'f' satisfies the relation f(x)f^('')(x)-f(x)f^(')(x) -f^(')(x)^(2)=0 AA x in R and f(0)=1=f^(')(0) . Then find f(x) .