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Question
Find the value of f(25), where f is a real function satisfying f(x + f(x)) = 5f(x) and f(1) =4.
Find the value of f(25), where f is a real function satisfying f(x + f(x)) = 5f(x) and f(1) =4.
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Solution
The correct option is C 100
We have f(x + f(x)) = 5 f(x)
Putting x = 1
f(1 + f(1)) = 5 f(1)
f(1 + 4) = 5 × 4
f(5) = 20
Now putting x = 5
f(5 + f(5)) = 5 f(5)
f(5 + 20) = 5* 20
f(25) = 100
We have f(x + f(x)) = 5 f(x)
Putting x = 1
f(1 + f(1)) = 5 f(1)
f(1 + 4) = 5 × 4
f(5) = 20
Now putting x = 5
f(5 + f(5)) = 5 f(5)
f(5 + 20) = 5* 20
f(25) = 100
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