Click to Chat

1800-1023-196

+91-120-4616500

CART 0

• 0

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
`        Hi allI have functional equation.Find the function such as f(0)=1/2 andexists a for any x,y f(x+y)=f(x)(a-y)+f(y)(a-x)I found that a=1/2 then f(x)=1/2-xIt seems OK, but test failed:f(x+y)=1/2-x-y andf(x)(1/2-y)+f(y)(1/2-x)=1/2-x-y+2xyI can't find the mistake (logical? calculation?)Ask for help.Thank you.`
one year ago

Pavan Kumar
32 Points
```							hiii, thank you for asking the question man,                   I don’t completely understand your problem but let me solve the problem and check your solution once again  f(x+y)=f(x)(a-y)+f(y)(a-x)                        -1             for  a=1/2 then f(x)=1/2-x                              also  f(y)=1/2-y                     substitute in -1                        we get    f(x+y)=f(x)(1/2-y)+f(y)(1/2-x)                                                 =(1/2-x)(1/2-y)+(1/2-y)(1/2-x)                                                  =2(1/2-x)(1/2-y)                                    f(0)=2*1/2*1/2=1/2            Hope you got your mistake and correct solution
```
one year ago
George
12 Points
```							Well, if the f(x)=1/2-x is the correct answer, then the left side of equationf(x+y)=f(x)(1/2-y)+f(y)(1/2-x)will be f(x+y)=1/2-x-y, but the right sidef(x)(1/2-y)+f(y)(1/2-x)=(1/2-x)(1/2-y)+(1/2-y)(1/2-x)=1/2-x-y+2xy
```
one year ago
Pavan Kumar
32 Points
```							Hey ,George at first i thought something else was your problem...this question has some many errors                                                 f(x+y)=f(x)(a-y)+f(y)(a-x)                        put y=0 gives                                        f(x)=f(x)(a)+f(0)(a-x)                                                  given f(0)=1/2 substitute it                                                f(x)=f(x)(a)+1/2(a-x)                                              so f(x)=    1/2*(a-x)/(1-a)   now here comes something wierd      f(x+y)=(a-x)(a-y)/(1-a)                                                              put y=a                                                              f(x+a)=0 this is wrong or else if  x and y not equal to a                                                             your contradiction so atleast they have to give a not equal to ½ and 1                                      see for the remaining conditions this contradiction will not come
```
one year ago
Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

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

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