Let f be the greatest integer function defined as f(x) = [x] and g be the modules function defined as

Question:

Let $f$ be the greatest integer function defined as $f(x)=[x]$ and $g$ be the modules function defined as $g(x)=|x|$, then the value of $g o f\left(-\frac{5}{4}\right)$ is  ___________.

Solution:

Given: f(x) = [x] and g(x) = |x|

$g \circ f\left(-\frac{5}{4}\right)=g\left(f\left(-\frac{5}{4}\right)\right)$

$=g\left(\left[-\frac{5}{4}\right]\right)$

$=g(-2)$

$=|-2|$

$=2$

Hence, the value of $g \circ f\left(-\frac{5}{4}\right)$ is 2 .

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