Show that if `f_1a n df_1` are one-one maps from `RtoR ,` then the product `f_1xf_2: RvecR` defined by `(f_1xf_2)(x)=f_1(x)f_2(x)` need not be one-one.

Show that if f_(1) and f_(2) are one-one maps from R to R, then the product f_(1)xx f_(2):R rarr R defined by (f_(1)xx f_(2))(x)=f_(1)(x)f_(2)(x) need not be one-one.

Give examples of two one-one functions f_(1)andf_(2) from R to R such that f_(1)+f_(2):RrarR defined by : (f_(1)+f_(2))(x)=f_(1)(x)+f_(2)(x) is not one-one.

Given examples of two one-one functions f_(1) and f_(2) from R to R such that f_(1)+f_(2):R rarr R, defined by (f_(1)+f_(2))(x)=f_(1)(x)+f_(2)(x) is not one- one.

Give examples of two one-one functions f_(1) and f_(2) from R to R such that f_(1)+f_(2):R rarr R , defined by (f_(1)+f_(2))(x)=f_(1)(x)+f_(2)(x) is not one-one.

f:R^(+)rarr R^(+) defined by f(x)=1+2x^(2) this function 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.

Prove that the function f:N rarr N, defined by f(x)=x^(2)+x+1 is one-one but not onto

Show that the function f:N rarr N given by f(1)=f(2)=1 and f(x)=x-1 for every x>=2, is onto but not one-one.

Suppose f_(1) and f_(2) are non=zero one-one functions from R to R .is (f_(1))/(f_(2)) necessarily one- one? Justify your answer.Here,(f_(1))/(f_(2)):R rarr R is given by ((f_(1))/(f_(2)))(x)=(f_(1)(x))/(f_(2)(x)) for all x in R.

Let f:RtoR be defined by f(x)=x/(1+x^2),x inR . Then the range of f is