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

If f(x) is periodic function of period t show that int_(a)^(a+t)f(x)dx is independent of a.

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

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

Which of the following function is/are periodic? A. f(x)={1,0,x is rationalx is irrational B. f(x)={x−[x],12,2n≤x<2n+12n+1≤x<2n+2 where [.] denotes the greatest integer function n∈Z C. f(x)=(−1)[2xπ, where [.] denotes the greatest integer function D. f(x)=x−[x+3]+tan(πx2), where [.] denotes the greatest integer function, and a is a rational number

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

The function f(x)=(sinx+cosx) is an increasing function in

If int(dx)/(x^2+a x+1)=f(g(x))+c , then f(x) is inverse trigonometric function for |a|>2 f(x) is logarithmic function for |a| 2 g(x) is rational function for |a|<2

Statement 1: The function f(x)=x^2+tan^(-1)x is a non-periodic function. Statement 2: The sum of two non-periodic functions is always non-periodic.

The period of the function f(x)= tan 4x is-