Question

If f:R→Rf:R→R and g:R→Rg:R→R are defined by f(x)=−[x]f(x)=−[x] and g(x)=[x]∀x∈R,f(g(x))=​

Answer 1

Answer:

We have, f(x)=x−[x]={x}…(1)

where {x} is the fractional part of x

If g(x)=[x], where [x] is the greatest integer part of x, then

The value of g(x) will always be an integer.

And ∴f(g(x))=f([x])=0

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