Prove that the function `f: R^(+) to R ` which is defined as `f(x)=log_(e) x ` 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.

Show that the function f: R to R defined by f(x)=2x^(2) , is neither one - one onto.

If R is the set of real numbers then prove that a function f: R to R defined as f(x)=(1)/(x), x ne 0, x in R, is one-one onto.

If R is the set of real numbers then prove that a function f: R to R defined as f(x)=(1)/(x), x ne 0, x in R, is one-one onto.

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

Determine whether the function f:(o,oo) to R defined by f(x) log_(e)x is one one (or)onto (or)bijection.

Show that the function f: R rarr R , defined as f(x) = x^2 , is neither one-one nor onto.

Prove that the function f : R to R defined by f(x) = 2x , AA x in R is bijective.