Let `R=(8+3sqrt(7))^20` and [.] denotes greatest integer function, then prove that :
(a) [R] is odd (b) R-[R] `=1-(1)/((8+3sqrt(7))^20`

Range of f(x)=[1/(log(x^(2)+e))]+1/sqrt(1+x^(2)), where [*] denotes greatest integer function, is

f(x)= [x] + sqrt(x -[x]) , where [.] is a greatest integer function then …….. (a) f(x) is continuous in R+ (b) f(x) is continuous in R (C) f(x) is continuous in R - 1 (d) None of these

Let S=sum_(r=1)^(117)(1)/(2[sqrtr]+1) , when [*] denites the greatest integer function and if S=(p)/(q) , when p and q are co-primes, the value of p+q is

Solve 1/[x]+1/([2x])= {x}+1/3where [.] denotes the greatest integers function and{.} denotes fractional part function.

Let f : R rarr R be defined as f(x) = 10 x +7 . Find the function g:R rarrR such that gof = fog = I_(g)

Let f : R rarr R be the Signum Function defined as f(x) = {(1,xgt0),(0,x = 0),(-1,xlt0):} and g : R rarr R be the Greatest Integer Function given by g(x) = [x] , where [x] is greatest integer less than or equal to x. Then , does fog and gof coincide in (0,1] ?

Prove that the following are irrationals (1) (1)/sqrt(2) (2) 7sqrt(5) (3)6+sqrt(2)

Prove that , ""^nP_r = ""^((n-1))Pr + r. ""^(n-1)P_((r-1))

Let f : R rarr R be the function defined by f(x) = 2x - 2 , AA x in R . Write f^(-1) .