4. (12) True or False. (1)f (x) 2x is onto where f: R.>R. (Note: R is the set of

Question

4. (12) True or False. (1)f (x) 2x is onto where f: R.>R. (Note: R is the set of real numbers) (2) f(x) = 2x is one-to-one where f: R-> R. (3) f(x) = x2 is onto where f: R-> R. (4) f(x) x2 is one-to-one where f: R >R (5) f(x) x2 is onto where f: R->[O, oo). (6) f(x) x* is one-to-one where f: R > [O,)

Explanation / Answer

Dear Student Thank you for using Chegg !! First of all, R -> R signifies all that x can take any values from R and corresponding to each value of x f(x) shall also have some value from R a) f(x) = 2x Here for each value of x, we shall be having a unique vallue of f(x) Hecne the function should be a one to odne function Therefore given statement is false. b) f(x) = 2x One to One TRUE c) f(x) = x^2 Here for each value of f(x) there can be two possible values of x (One positive and one negative) Hence clearly given function is ONTO TRUE d) f(x) = x^2   , R ->R As described in part C above, given function is onto in R -> R Hence its not one to one FALSE. e) f(x) = x^2 for X belongs to 0 to infinity Here since x cannot take any negative values, hence the given function is one to one for all positive x FALSE f) As described in part e, function is one to odne for all positive x TRUE

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.