Let `f(sinx) + 2f(cos x) =3` for all `x in R`. Fird `f(x)`

Let f(x) = sin (pi/6 sin (pi/2 sinx)) for all x inR and g(x) = pi/2 sinx for all x in R . Let (fog)(x) dentoe f(g(x)) and (gof)(x) denote g(f(x)). Then which of the following is (are) True?

Let the function f:9R to 9R be defined by f(x)=2x+sin for all x in 9R . Then f(x) is

Let g(x) =f(x)-2{f(x)}^2+9{f(x)}^3 for all x in R Then

Let g(x) =f(x)-2{f(x)}^2+9{f(x)}^3 for all x in R Then

Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f '(x) ne 0 for all x in R . If |[f(x)" "f'(x)], [f'(x)" "f''(x)]|= 0 , for all x in R , then the value of f(1) lies in the interval:

Let f(x+y)=f(x)+f(y) for all real x,y and f'(0) exists.Prove that f'(x)=f'(0) for all x in R and 2f(x)=xf(2)

Let f:R rarr R be a twice differentiable function such that f(x+pi)=f(x) and f'(x)+f(x)>=0 for all x in R. show that f(x)>=0 for all x in R .

Let f: R to R : f (x) = 4x+3 for all x in R . Show that f is invertible and find f^(-1)