Let `f: R->R` be a continuous function and `f(x)=f(2x)` is true `AAx in R`. If `f(1)=3,` then the value of `int_(-1)^1f(f(x))dx` is equal to

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)

A continuous real function f satisfies f(2x)=3f(x)AAx in RdotIfint_0^1f(x)dx=1, then find the value of int_1^2f(x)dx

If f(x)=min(|x|,1-|x|,1/4)AAx in R , then find the value of int_(-1)^1f(x)dxdot

If a continuous function f on [0, a] satisfies f(x)f(a-x)=1, a >0, then find the value of int_0^a(dx)/(1+f(x))

Let f : R rarr R be a continuous function which satisfies f(x) = int_0^x f(t) dt . Then the value of f(log_e 5) is

Let f: R to R be a continuous function which satisfies f(x)= int_0^xf(t)dtdot Then the value of f(1n5) is______

Let f:R to R be a differentiable function and f(1)=4 and f'(1)=2 , then the value of lim_(x to 1) int_(4)^(f(x))(2t)/(x-1)dt is -

f:R^+ ->R is a continuous function satisfying f(x/y)=f(x)-f(y) AAx,y in R^+ .If f'(1)=1,then (a)f is unbounded (b) lim_(x->0)f(1/x)=0 (c) lim_(x->0)f(1+x)/x=1 (d) lim_(x->0)x.f(x)=0

let T le0 be a fixed real number suppose f is continuous function such that for all x in R f(x+T)=F(x) if I=int_0^T f(x)dx then the value of int_3^(3+3T)f(2x)dx is

Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)fora l lx in [-1,2]dot Let R_1=int_(-1)^2xf(x)dx , and R_2 be the area of the region bounded by y=f(x),x=-1,x=2, and the x-axis . Then (a) R_1=2R_2 (b) R_1=3R_2 (c) 2R_1 (d) 3R_1=R_2