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The function `f` satisfies the functional equation `3f(x)+2f((x+59)/(x-1))=10 x+30` for all real `x!=1.` The value of `f(7)i s` (a) 8 (b) 4 (c) `-8` (d) 11

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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