If f be the greatest integer function and g be the modulus functi… - Vidyadip

MCQ

If $f$ be the greatest integer function and $g$ be the modulus function, then $(gof)\left( { - \frac{5}{3}} \right) - (fog)\left( { - \frac{5}{3}} \right) = $

✓
$1$
B
$-1$
C
$2$
D
$4$

✓

Answer

Correct option: A.

$1$

a
(a) Given $(gof)\,\,\left( {\frac{{ - 5}}{3}} \right) - (fog)\,\left( {\frac{{ - 5}}{3}} \right)$

$ = g\,\left\{ {f\left( {\frac{{ - 5}}{3}} \right)} \right\} - f\left\{ {g\left( {\frac{{ - 5}}{3}} \right)} \right\} = g( - 2) - f\left( {\frac{5}{3}} \right) = 2 - 1 = 1$ .

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