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 rarr R be defined by f(x)=2x+sin x 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

Show that the function f:R rarr R defined by f(x)=(x)/(x^(2)+1)AA x in R is neither one-one nor onto.Also if g:R rarr R is defined by g(x)=2x-1 find fog(x)

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 rarr R given by f(x)=cos x for all x in R, is neither one- one nor onto

Is the function f:R rarr R be defined by f(x)=2x+3 a one on one function?

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 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.

Let the function f: R-{-b}->R-{1} be defined by f(x)=(x+a)/(x+b) , a!=b , then (a) f is one-one but not onto (b) f is onto but not one-one (c) f is both one-one and onto (d) none of these