The function f(x) is discontinuous only at x = 0 such that `f^(2)(x)=1 AA x in R`. The total number of such functions is

The function f(x)=(sinx)/(sinx-cosx) is discontinuous at -

If f(x) is a function such that f'(x)=(x-1)^(2)(4-x) then,

In the function f(x) is defined for x in[0,1] then the function f(2x+3) is defined for

Let f(x)={8^(1/x),x<0a[x],a in R-{0},xgeq0, (where [.] denotes the greatest integer function). Then (a) f(x) is Continuous only at a finite number of points (b)Discontinuous at a finite number of points. (c)Discontinuous at an infinite number of points. (d)Discontinuous at x=0

If f(x) is a function such that f'(x)= (x-1)^2 (4-x) , then

If the function f: R- {0}-> R given by f(x)=1/x-2/(e^(2x)-1) is continuous at x=0, then find the value of f(0)

If the function f(x) satisfies the condition f(x + 1/x) = x^2 + 1/x^2,x ne 0 then f(x) is

The function f:R to R is defined by f(x)=cos^(2)x+sin^(4)x for x in R . Then the range of f(x) is

A function f (x) is defined as follows: f(x)={{:(x+2,"when "xlt2),(x^(2)-1,"when "xge2):} Show that f (x) is discontinuous at x = 2 and the jump of the function at this point is -1 .