Question 1196484
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If f(2a-b) = f(a)*f(b) for all a and b, and the function is never equal to zero, 
find the value of f(5).
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            Let solve the problem in 4 (four) steps.



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(a)  Let a = 1, b = 1.  Then, according to the given formula, 

     f(2*1-1) = f(1)*f(1),    or

     f(1)     = f(1)*f(1). 

     Since f(1) =/= 0  (as it is given),  it implies  f(1) = 1   (we can cancel the common factor f(1) in both sides).



(b)  Let a = 1, b = 2.  Then, according to the given formula, 

     f(2*1-1) = f(1)*f(2),    or

     f(1)     = f(1)*f(2).

     Since f(1) = 1 (we just know it from (a)),  it implies f(2) = 1.



(c)  Let a = 2, b = 1.  Then, according to the given formula, 

     f(2*2-1) = f(2)*f(1),    or

     f(3)     = 1*1 = 1      (since we just know from (b) and (a) that f(2) = 1, f(1) = 1 ).



(d)  Let a = 3, b = 1.  Then, according to the given formula, 

     f(2*3-1) = f(3)*f(1),    or

     f(5)     = 1*1 = 1      (since we just know from (c) and (a) that f(3) = 1, f(1) = 1 ).
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Thus we just found out that f(5) = 1, and the solution is complete at this point.