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

If f(x)a n dg(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 (a) 177 (b) 222 (c) 433 (d) 1155

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

Which of the following function is/are periodic? (a)f(x)={1,xi sr a t ion a l0,xi si r r a t ion a l (b)f(x)={x-[x]; 2n

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.

TRUE/FALSE: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.

Discuss whether the function f(x)="sin"(cosx+x) is period or not. If yes, then what is its period?

Statement 1 : For a continuous surjective function f: RvecR ,f(x) can never be a periodic function. Statement 2: For a surjective function f: RvecR ,f(x) to be periodic, it should necessarily be a discontinuous function.

Suppose that f is even, periodic function with period 2, and that f(x) = x for all x in the interval [0, 1]. Then draw the graph of y = f(x).

Statement 1: If differentiable function f(x) satisfies the relation f(x)+f(x-2)=0AAx in R , and if ((d/(dx)f(x)))_(x=a)=b ,t h e n((d/(dx)f(x)))_(a+4000)=bdot Statement 2: f(x) is a periodic function with period 4.

Suppose that f is an even, periodic function with period 2,a n dt h a tf(x)=x for all x in the interval [0,1] . The values of [10f(3. 14)] is(where [.] represents the greatest integer function) ______