Let `f: RrarrR,` where `f(x)=sinx ,` Show that f is into.

Let f: NvecZ be a function defined as f(x)=x-1000. Show that f is an into function.

Let the function f: RrarrR be defined by f(x)=2x+sinx for x in Rdot 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

Let A be the set of all 50 students of Class X in a school Let f: A to N be function defined by f(x) = roll number of the student x. Show that f in one-one but not onto.

Prove that f(x)=x-sinx is an increasing function.

Let f:Rto"be defined by"f(x)=1absx. Then the range of f is

Let f:RrarrR be such that f(a)=1, f(a)=2 . Then lim_(x to 0)((f^(2)(a+x))/(f(a)))^(1//x) is

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot