Test (elaborations) mathematics on functions part 2
5 views 0 purchase
Course
Mathematics
Institution
Certainly! Let’s dive into the topic of functions, which is crucial for JEE preparation. . This is the part 2 on questions of functions which are of very high tough level. if you already have solved part 1 then, CONGRATULATIONS!!!!! . Now get started with part 2 and show yourself the maths pro!!!...
1. If f(x) = x3+3x2 + 12x−2 sinx, where f: R →R, then
(a) f(x) is many-one and onto (b) f(x) is one-one and onto
(c) f(x) is one-one and into (d) f(x) is many-one and into
2. Let function f: R→ R be defined by f(x) =2x+sin x for x ∈R. Then, f is
(a) One-one and onto (b) One-one but not onto
(c) Onto but not one-one (d) Neither one-one nor onto
𝑥
3. If f:[0, ∞) →[0, ∞) and f(x)= then f is:
1+𝑥
(a) One-one and onto (b) One-one but not onto
(c) Onto but not one- one (d) Neither one-one nor onto
4. The function f: [0, 3] →[1, 29], defined by f(x)=2x3−15x2+36x+1, is
(a) One-one and onto (b) Onto but not one-one
(c) One-one but not onto (d) Neither one-one nor onto
5. For real x, let f(x)= x3+5x+1, then
(a) f is onto R but not one-one (b) f is one-one and onto R
(c) f is neither one-one nor onto R (d) f is one-one but not onto R
6. A function f from the set of natural numbers to integers defined by
𝑛−1
, when n is odd
𝑓 (𝑛) = { 2𝑛
– , when n is even
2
(a) neither one-one nor onto (b) one-one but not onto
(c) onto but not one-one (d) one-one and onto both
7. Let f: N → 𝑌 be a function defined as f(x)=4x+3 where y= {y ∈ 𝑁: y=4x+3 for some x ∈N}. f is
invertible and its inverse is
3𝑦+4 𝑦−3 𝑦+3 𝑦−3
(a) g(y)= (b)g(y)=4+ (c) g(y)= (d) g(y)=
3 4 4 4
8. If the function f(x) and g(x) are defined on R →R such that
0, x ∈ rational 0, x ∈ irrational
f(x)= { ; g(x) = {
x, x ∈ irrational x, x ∈ rational
Then (f−g) (x) is
(a) one-one and onto (b) neither one-one nor onto
(c) one-one but not onto (d) onto but not one-one
9. Let 𝐸 = {1, 2, 3, 4} and 𝐹 = {1,2}. Then, the number of onto functions from E to F is
(a) 14 (b) 16 (c) 12 (d) 8
10. If the function 𝑓: R→ R is defined by 𝑓 (𝑥) = |𝑥|(𝑥 − 𝑠𝑖𝑛 𝑥), then which of the following statements
is TRUE? (2020 Adv.)
(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) 𝑓 is NEITHER one-one NOR onto
1
11. Let a function 𝑓: (0, ∞) → (0, ∞) be defined by 𝑓(𝑥) = |1 − 𝑥 |. Then, 𝑓 is
(a) injective only (b) both injective as well as surjective
(c) not injective but it is surjective (d) neither injective nor surjective
E2C Maths Forum
By: ER. Ashok Kumar
Trained from Renowned Institute, KOTA (RAJ.)
Address : Beside Siliguri Child Welfare Society, Baghajatin Park, Siliguri, Contact No : 9046278670
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Arinjoydey07. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $7.69. You're not tied to anything after your purchase.
