Let `f: R rarr R `, where `f(x) = sinx` , Show that f is into

Consider f : R rarr R given f(x) = 4x + 3. Show that f is invertible. Find the inverse of f.

If f : R rarr S , defined f(x) = sin x - sqrt3cos x+1 is onto , then find the set S

Let f: R rarr R where f(x) = (x^2+4x+7)/(x^2+x+1) Is f(x) one - one ?

Let f: (2,4) rarr (1,3) where f(x) = x - [x//2] (where [ .] denotes the greatest integer function), then f^(-1)(x) is

If f:R rarr R , f(x)=x+3. Then find fof(1)

Let N rarr R be a function defined as f(x) = 4x^2 + 12x +15 Show that f : N rarr S , where, S is the range of f, is invertible. Find the inverse of f.

Show that the modulus function f: R rarr R given by f(x) = |x| , is neither one-one nor onto.

Let R be the set of real numbers. Define the real function. f: R rarr R by f(x)=x+1 0 and sketch the graph of this function.

Let the function f:R rarr R be defined by f (x) = 2x + sinx for x in R .Then f is a)one - to - one and onto b)one - to - one but not onto c)onto but not one - to - one d)neither one - to - one nor onto

Let f : X rarr Y be invertible, show that the inverse of f^(-1) = f, i.e., (f^(-1))^(-1) = f .