Let `f:X to Y` be an invertible function. Show that f has uniques inverse.

Let f : X to Y be an invertible function. Show that the inverse of f ^(-1) is f, i.e., (f ^(-1)) ^(1)=f.

Let the function f:R to R be defined by f(x)=cos x, AA x in R. Show that f is neither one-one nor onto.

Let f:(-1,1)toR be a differentiable function with f(0)=-1 and f'(0)=1 . Let g(x)=[f(2f(x)+2)]^(2) . Then g'(0)=

Let f be twice differentiable function such that f^('')(x) = -f(x) and f^(')(x) = g(x) . Also h(x) = [f(x)]^(2) + [g(x)]^(2). If h(4) = 7, then h(7) =

The function f(x)=|x| has:

Let f : N to R be defined by f(x) = 4x^(2) + 12x + 15 , show that f: N to S , where S is the function, is invertible. Also find the inverse.

Let f:NtoY be a function defined as f(x)=4x+3 , where Y={yinN,y=4x+3 for some x inN }. Show that f is invertible and its inverse is :

Let f: N to R be defined by f(x) = 4x^(2) + 12x+ 15 . Show that f: N to S where S is the range of function f, is invertible. Also find the inverse of f.