Let `f: R->R` be a function such that `f(x)=a x+3sinx+4cosxdot` Then `f(x)` is invertible if (a)`a in (-5,5)` (b) `a in (-oo,5)` (c)`a in (-5,+oo)` (d) none of these

Let f:R->R be a continuous function such that |f(x)-f(y)|>=|x-y| for all x,y in R ,then f(x) will be

Let f(x) be a function such that f(x)=(log)_(1/2)[(log)_3(sinx+a]dot If f(x) is decreasing for all real values of x , then a in (1,4) (b) a in (4,oo) a in (2,3) (d) a in (2,oo)

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Given that f'(x) > g'(x) for all real x, and f(0)=g(0) . Then f(x) < g(x) for all x belong to (a) (0,oo) (b) (-oo,0) (c) (-oo,oo) (d) none of these

If R->R is an invertible function such that f(x) and f^-1(x) are symmetric about the line y=-x, then (a) f(x) is odd (b) f(x) and f^-1(x) may be symmetric (c) f(c) may not be odd (d) non of these

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then f(x) is an increasing function in (0,oo) f(x) is a decreasing function in (-oo,oo) f(x) is an increasing function in (-oo,oo) f(x) is a decreasing function in (-oo,0)

The domain of the function f(x)=sqrt(x^2-[x]^2) , where [x] is the greatest integer less than or equal to x , is (a) R (b) [0,+oo) (c) (-oo,0) (d) none of these

Let f(x) be a quadratic expression such that f(-1)+f(2)=0 . If one root of f(x)=0 is 3 , then the other root of f(x)=0 lies in (A) (-oo,-3) (B) (-3,oo) (C) (0,5) (D) (5,oo)

Let f be a function f:N→N be defined by f(x)=5x-3 , Find the image of 3,4,5 .

Let f: R->R be a continuous function and f(x)=f(2x) is true AAx in Rdot If f(1)=3, then the value of int_(-1)^1f(f(x))dx is equal to (a)6 (b) 0 (c) 3f(3) (d) 2f(0)