Let `f: N->Z` be a function defined as `f(x)=x-1000.` Show that `f` is an into function.

Let f: R to R be a function defined as f (x) = 3x+ 7 , x in R . Show that f is an onto functions.

Let f:Xrarr Y be a function defined by f(x)=sinx .

If f: R->R be the function defined by f(x)=4x^3+7, show that f is a bijection.

If f: R->R be the function defined by f(x)=4x^3+7 , show that f is a bijection.

Let f: N -> S be a function defined as f(x)=9x^2+6x-5 . Show that f:N -> S, where S is the range of f , is invertible. Find the inverse of f and hence f^(-1)(43) and f^(-1)(163)

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

Prove that the function defined by f(x) = t a n x is a continuous function.

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

If f: RvecR be the function defined by f(x)=4x^3+7, show that f is a bijection.

Let f: NvecR be a function defined as f(x)=4x^2+12 x+15. Show that f: NvecS , where S is the range of f, is invertible. Also find the inverse of f