Let `f(x)=x+f(x-1)forAAx in RdotIff(0)=1,fin df(100)dot`

Let f(x)=x+f(x-1) where x varepsilon R. If F(0)=1 find f(100)

Let Q(x)=f(x)+f(1-x) and f'(x)<0,0<=x<=

Let f:R rarr R be a differentiable and strictly decreasing function such that f(0)=1 and f(1)=0. For x in R, let F(x)=int_(0)^(x)(t-2)f(t)dt

Let g(x)=1+x-[x] and f(x)=-1 if x 0, then f|g(x)]=1x>0

Let f(x)=(x-1)/(x+1) then f(1) is equal to

Let the function f be defined by f (x) = |x-1| -1/2, 0 le x le 2, f (x +2 ) = f (x) for all x in R. Evaluate (i) int _(0) ^(100) f (x) dx (ii) int _(0) ^(1)| f(2x ) |dx

Let f defined on [0,1] be twice differentiable such that |f(x)|<=1 for x in[0,1], if f(0)=f(1) then show that |f'(x)<1 for all x in[0,1]

Let f(x)=x^(3)/3-x^(2)/2+x-16 . Find f^(')(0), f^(')(-1) .

Let f:R rarr R be a function defined by f(x)=|x] for all x in R and let A=[0,1) then f^(-1)(A) equals