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The function `f` satisfies the functional equation `3f(x)+2f((x+59)/(x1))=10 x+30` for all real `x!=1.` The value of `f(7)i s` If `f(x+y)=f(x)+f(y)-x y-1`, `AA x , `y in R ` and `f(1)=1,` then the number of solution of `f(n)=n` , `n in N ,` is

A

8

B

4

C

-8

D

11

Text Solution

Verified by Experts

The correct Answer is:
B
`3f(x)+2f((x+59)/(x-1))=10x+30`
For `x=7, 3f(7)+2f(11)=70+30=100.`
For `x=11, 3f(11)+2f(7)=140.`
`(f(7))/(-20)=(f(11))/(-220)=(-1)/(9-4) or f(7)=4`
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