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Functional Equation (Tomato subjective 64)

Problem: If f(x) is a real-valued function of a real variable x, such that 2f(x) + 3f(-x) = 15 – 4x for all x, find the function f(x).
Solution: 2f(x) + 3f(-x) = 15 – 4x
Putting x =0, we gets
2f(0) + 3f(0) = 15
Or f(0) = 3.
Let g(x) = f (x) – 3
2f(x) + 3f(-x) = 15 – 4x
Or 2g(x) + 3g(-x) = – 4x …(i)

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June 15, 2015

1 comment

  1. In the original equation if we put x=-x then we will have two equations in f(x) and f(-x). and then we can solve the two equations and find f(x)=4x+3

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