Let` f(x) = x/(e^x -1) +x/2 +1` , then f(x) is
1. even
2. odd
3. periodic
4. none

Let f(x) = x - [x] , x in R then f(1/2) is

Let f(x)=log_(e)|x-1|, x ne 1 , then the value of f'((1)/(2)) is

If f(x) = |(a, -1, 0), (ax, a,-1 ) ,(ax^(2), ax, a)| , then f(2x)-f(x) is divisible by 1) a 2) b 3) c ,d ,e 4). none of these

If f(2+x)=a+[1-(f(x)-a)^4]^(1/4) for all x in R ,then f(x) is periodic with period

Let f(x)=(e^(x))/(1+x^(2)) and g(x)=f'(x) , then

Let f (x)=|x-2|+|x - 3|+|x-4| and g(x) = f(x+1) . Then 1. g(x) is an even function 2. g(x) is an odd function 3. g(x) is neither even nor odd 4. g(x) is periodic

Let f (x) = a ^ x ( a gt 0 ) be written as f ( x ) = f _ 1 (x ) + f _ 2 (x) , where f _ 1 ( x ) is an even function and f _ 2 (x) is an odd function. Then f _ 1 ( x + y ) + f _ 1 ( x - y ) equals :

If f(x)={x^2sin(pix)/2,|x|<1x|x|,|x|geq1,t h e nf(x)i s an even function (b) an odd function a periodic function (d) none of these

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)=(x-1)^4(x-2)^n ,n in Ndot Then f(x) has (a) a maximum at x=1 if n is odd (b) a maximum at x=1 if n is even (c) a minimum at x=1 if n is even (d) a minima at x=2 if n is even