Let `f(x)` be a continuous function defined for `1 <= x <= 3.` If `f(x)` takes rational values for all `x and f(2)=10` then the value of `f(1.5)` is :

Let f(x) be a continuous function defined for AA x in R , if f(x) take rational values AA x in R and f(2) = 198 , then f(2^(2)) = ……

Let f(x) be a continuous function defined for 0lexle3 , if f(x) takes irrational values for all x and f(1)=sqrt(2) , then evaluate f(1.5).f(2.5) .

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

Let f(x)a n dg(x) be two continuous functions defined from RvecR , such that f(x_1) > f(x_2) and g(x_1) x_2 dot Then what is the solution set of f(g(alpha^2-2alpha) > f(g(3alpha-4))

Property 8: If f(x) is a continuous function defined on [-a; a] then int_(-a) ^a f(x) dx = int_0 ^a {f(x) + f(-x)} dx

Let [x] denote the integral part of x in R and g(x) = x- [x] . Let f(x) be any continuous function with f(0) = f(1) then the function h(x) = f(g(x) :

Let f(x) be a continuous function and I = int_(1)^(9) sqrt(x)f(x) dx , then

Let f(x) be a continuous function in R such that f(x) does not vanish for all x in R . If int_1^5 f(x)dx=int_-1^5 f(x)dx , then in R, f(x) is (A) an even function (B) an odd function (C) a periodic function with period 5 (D) none of these

Let f(x) be a continuous function, AA x in R, f(0) = 1 and f(x) ne x for any x in R , then show f(f(x)) gt x, AA x in R^(+)

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