iff:R gives Q(rational),g:R gives Q(rational) are two continuous functions suchthat(square root of 3)f(x)+g(x0=4 ,then (1-f(x))3+(g(x)-3)3 is equal to

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dear student, the complete ignorance and lunacy shown by some members as Vikas and saurabh is totally uncalled for. In my earlier ans, he deems my ans as substandard. i dont like to be challenged by amateur and incompetent people like him in mathematics. he is a joke for a tutor.

CORRECT SOL:

sqrt(3)f(x)= 4 – g(x)

now, assume that f(x) is not zero at least for some x= x0

then, sqrt3= (4 – g(x0))/f(x0)

however, f and g can only take rational values, hence (4 – g(x0))/f(x0) must also be rational, which is impossible since sqrt3 is irrational.

hence, f(x)= 0 for all x

so that g(x)= 4 for all x.

so (1-f(x))³  +(g(x)-3)³= 1^3 + 1^3

= 2