Let `f` be a continuous function defined onto [0,1] with range [0,1]. Show that there is some `c` in [0,1] such that `f(c)=1-c`

If f is a continuous function on [0,1], differentiable in (0, 1) such that f(1)=0, then there exists some c in (0,1) such that cf^(prime)(c)-f(c)=0 cf^(prime)(c)+cf(c)=0 f^(prime)(c)-cf(c)=0 cf^(prime)(c)+f(c)=0

Leg f be continuous on the interval [0,1] to R such that f(0)=f(1)dot Prove that there exists a point c in [(0,1)/2] such that f(c)=f(c+1/2)dot

Let fa n dg be differentiable on [0,1] such that f(0)=2,g(0),f(1)=6a n dg(1)=2. Show that there exists c in (0,1) such that f^(prime)(c)=2g^(prime)(c)dot

Let f and g be function continuous in [a,b] and differentiable on [a,b] .If f(a)=f(b)=0 then show that there is a point c in (a,b) such that g'(c) f(c)+f'(c)=0 .

The function f(x) is defined in [0,1] . Find the domain of f(tanx).

The function f(x) is defined in [0,1] . Find the domain of f(t a nx)dot

Let f be a function defined on [0,2]. Then find the domain of function g(x)=f(9x^2-1)

Let f be a continuous function satisfying f '(I n x)=[1 for 0 1 and f (0) = 0 then f(x) can be defined as

If f is continuous and differentiable function and f(0)=1,f(1)=2, then prove that there exists at least one c in [0,1]forw h i c hf^(prime)(c)(f(c))^(n-1)>sqrt(2^(n-1)) , where n in Ndot

Let f:[0,1] rarr [0,1] be a continuous function. Then prove that f(x)=x for at least one 0lt=xlt=1.