Determine f(3) if f(3x)+3*f(-3x)=x+1

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We have to find f(3) given that f(3x) + 3*f(-3x) = x + 1

f(3x) + 3*f(-3x) = x + 1

for x = 1

=> f(3) + 3*f(-3) = 1 + 1 = 2 ...(1)

for x = -1

=> f(-3) + 3*f(3) = 0 ...(2)

(1) - 3*(2)

...

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We have to find f(3) given that f(3x) + 3*f(-3x) = x + 1

f(3x) + 3*f(-3x) = x + 1

for x = 1

=> f(3) + 3*f(-3) = 1 + 1 = 2 ...(1)

for x = -1

=> f(-3) + 3*f(3) = 0 ...(2)

(1) - 3*(2)

=> f(3) + 3*f(-3) - 3*f(-3) - 9*f(3) = 2

=> f(3) - 9*f(3) = 2

=> -8*f(3) = 2

=> f(3) = -1/4

The required value of f(3) = -1/4

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