`f(x)=(x+1)^(3)-(x-1)^(3)` represents a functions which is

Show that the function f(x)=x^(3)+1/(x^(3)) is decreasing function in the interval [-1,1]-{0} .

Find the intervals on which the function f(x) = (x + 1)^(3) (x -3)^(3) is (a) increasing (b) decreasing

For x in R-{0,1}, " let " f_(1)(x)=(1)/(x), f_(2)(x)=1-x and f_(3)(x)=(1)/(1-x) be three given functions. If a function, J(x) satisfies (f_(2) @J@f_(1))(x)=f_(3)(x), " then " J(x) is equal to

For x in R-{0,1}, " let " f_(1)(x)=(1)/(x), f_(2)(x)=1-x and f_(3)(x)=(1)/(1-x) be three given functions. If a function, J(x) satisfies (f_(2) @J@f_(1))(x)=f_(3)(x), " then " J(x) is equal to

For x in R-{0,1}, let f_(1)(x)=(1)/(x),f_(2)(x)=1-x and f_(3)(x)=(1)/(1-x) be three given functions.If a function,J(x) satisfies (f_(2)oJof_(1))(x)=f_(3)(x) then J(x) is equal to

Show that the function f(x)= x^(3) - 3x^(2)+3x - 1 is an increasing function on R.

Show that the function f(x)= x^(3) - 3x^(2)+3x - 1 is an increasing function on R.

Discuss the differentiability of f(x)=[x]+|1-x|,x in(-1,3), where [.] represents greatest integer function.

The domain of the function f (x) = sin^(-1)((1+x^3)/(2x^(3/2)))+sqrt(sin(sinx))+log_(3{x}+1)(x^2+1) , where {.} represents fractional part function, is: