Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Grade: 12

                        

Let the function f: R → R be defined by f (x) = cos x, ∀ x ∈ R. Show that f is neither one-one nor onto.

 Let the function f: R → R be defined by f (x) = cos x, ∀ x ∈ R. Show that f is neither one-one nor onto. 

4 months ago

Answers : (1)

Anand Kumar Pandey
askIITians Faculty
4182 Points
							Dear Student

We have,
f: R → R, f(x) = cos x
Now,
f (x1) = f (x2)
cos x1= cos x2
x1=2nπ±x2,n∈Z
It’s seen that the above equation has infinite solutions for x1and x2Hence, f(x) is many one function.
Also the range of cos x is [-1, 1], which is subset of given co-domain R.
Thus,the given function is not onto.
Thanks
4 months ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 731 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 53 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts
 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details