If `f(x)=sinx+cosa x` is a periodic function, show that `a` is a rational number

If f(x)=cosx+cosa x is periodic function, then a must be (a)an integer (b) a rational number (c)an irrational number (d) an even number

If f(x) is a continuous function such that its value AA x in R is a rational number and f(1)+f(2)=6 , then the value of f(3) is equal to

If f(x) is periodic function with period, T, then

If f(x+10) + f(x+4)= 0 , there f(x) is a periodic function with period

If f(x) is an odd periodic function with period 2, then f(4) equals to-

If f(x) and g(x) are periodic functions with periods 7 and 11, respectively, then the period of f(x)=f(x)g(x/5)-g(x)f(x/3) is

Statement-1 : f(x) = [{x}] is a periodic function with no fundamental period. and Statement-2 : f(g(x)) is periodic if g(x) is periodic.

Prove that f(x)=x-sinx is an increasing function.

The function f(x)=|cos| is periodic with period

Let f(x, y) be a periodic function satisfying f(x, y) = f(2x + 2y, 2y-2x) for all x, y; Define g(x) = f(2^x,0) . Show that g(x) is a periodic function with period 12.