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
Menu
Grade: 12
        
Given y^3+3y=x. Prove that y=f(x) is a single valued function in x.
7 months ago

Answers : (1)

Aditya Gupta
1145 Points
							
Consider f(y)= y^3+3y-x
Let us assume x is a particular constant.
Then f'(y)= 3y^2+3 which is always greater than zero.
So since f(y) is a cubic in y, it is bound to have atleast one root, but since it is also an increasing function, hence there will be exactly one root.
Therefore for any real x there exists one and only real root of f(y). So f(y)=0 for single y only.
Or y^3+3y=x is a single valued function.
7 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

  • 51 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

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details