Asked by Sandeep Kumar

Could anyone, please, help me solve this?

Let f be a function with the domain the set of all real numbers except 0 and 1 ,that satifies the equation :

2xf(x) - f[(x-1)/x] = 20

Find f(5/4)
Answered by oobleck
note that (x-1)/x = 5/4 if x = -4
Now you have
2(5/4)f(5/4) - f(1/5) = 20
2(1/5)f(1/5) - f(-4) = 20
2(-4)f(-4) - f(5/4) = 20
Now just solve for f(5/4)
Answered by Sandeep Kumar
-8f(-4)-f(5/4)=20
or f(5/4)= -8f(-4)-20
Now what to do with f(-4)? How to find it?
Answered by oobleck
come on. Didn't you read what I gave you? Suppose you let
x = f(5/4)
y = f(1/5)
z = f(-4)
Now you just have to find x when you have
5/2 x - y = 20
2/5 y - z = 20
-8z - x = 20
Three equations in three unknowns.
Answered by Sandeep Kumar
Actually I didn't read it thoroughly and quickly replied you. Then I left the site and kept trying to solve it. I got the answers. Now I just came back and saw your replies, which is exactly the same method.
Thank you for your help.
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