Show `f:R rarr R " defined by " f(x)=x^(2)+x " for all " x in R` is many-one.

Show f:R rarr R defined by f(x)=x^(2)+4x+5 is into

If f: R rarrR is defined by f(x) =x^(2)-3x+2 , find f(f(x)).

Let the function f : R rarr R be defined by f(x) = cos x , AA x in R . Show that f is nether one - one nor onto .

Show that the function f : R rarr R , defined by f(x) =1/x is one - one and onto , where R is the set of all non - zero real number . is the result true, if the domain R is replaced by N with co-domain being same as R ?

Show that the function f : R rarr {x inR:-1lt x lt1} defined by f(x) =x/(1+|x|),x in R is one one and onto function.

Let f:R rarr R defined by f(x)=(x^(2))/(1+x^(2)) . Proved that f is neither injective nor surjective.

If f,g : R rarr R be defined by f(x) = 2x + 1 and g(x) =x^(2) -2 , AA x in R , respectively . Find gof .

f : R rarr R , f(x) = x^(2) +2x +3 is .......