A mapping `f: R -> R` such that `f(x) = 2x +1AA x in R`. Prove that `f` is one-one.

A function f: R to R is defined as f(x)=4x-1, x in R, then prove that f is one - one.

A function f: R to R is defined as f(x)=4x-1, x in R, then prove that f is one - one.

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 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 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 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 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 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.

If a function f: R to R is defined as f(x)=x^(3)+1 , then prove that f is one-one onto.

If R is the set of real numbers and a function f: R to R is defined as f(x)=x^(2), x in R , then prove that f is many-one into function.