Question

If f(x) = [x] and g(x) = |x|, then evaluate:
1.(fog)(5/2)-(Gof)(-5/2)
relations and functions​

Answer 1

$Answer \: \: \\ \\ GIVEN \: \: QUESTION \: \: Is \: \: \: \\ \\ f(x) = (x) \: \: \: \: and \: \: \: g(x) = |x| \\ \\ fog( \frac{5}{2} ) = f(g( \frac{5}{2} )) \\ \\ fog( \frac{5}{2} ) = f( | \frac{5}{2} | ) \\ \\ fog( \frac{5}{2} ) = ( \frac{5}{2} ) \\ \\ fog( \frac{5}{2} ) = (2.5) \\ \\ fog (x) = 2 \: \: \: ... \: \: i\\and \\ gof( \frac{ - 5}{2} ) = g(f( - 2.5)) \\ \\ gof( \frac{ - 5}{2} ) = g( - 3) \\ \\ gof( \frac{ - 5}{2} ) = | - 3| \\ \\ gof( \frac{ - 5}{2} ) = 3 \: \: \: .... \: ii \\ \\ from \: i \: and \: ii \: we \: have \\ \\ fog( \frac{5}{2} ) - gof( \frac{ - 5}{2} ) = - 1 \\ \\ Note \: \: \: \: \: \: \: \: \\ \\ 1) \: \: \: here \: \: () \: \: \\ Repsents \: \: gif \\ \\ 2) \: \: \: if \: \: \: ( - x) = - (x) \: \: \: \: when \: \: x \: is \: an \: \\ integer \: \\ ( - x) = - (x) - 1 \: \: \: when \: x \: is \: not \: \\ an \: integer \:$