Question

If $\mathrm{f}$ be a greatest integer function and $\mathrm{g}$ be an absolute value function. Find the value of $\text { (log) }\left(\frac{-3}{2}\right)+(\text { gof })\left(\frac{4}{3}\right) \text {. }$

Answer 1

SOLUTION : Here $f(x)=[x] g(x)=|x|$

$\text { (fog) } x=f(g(x))=f(|x|)=[|x|] \\$

$\therefore \quad\left(\text { fog) }\left(\frac{-3}{2}\right)=\left[\left|\frac{-3}{2}\right|\right]=\left[\frac{3}{2}\right]=1 \quad \Rightarrow \quad(g \circ f) x=g(f(x))=g([x])=|[x]|\right. \\$

$\therefore \quad \text { (gof) }\left(\frac{4}{3}\right)=\left[\frac{4}{3}\right]|=| 1 \mid=1 \quad \Rightarrow \quad(\text { fog })\left(\frac{-3}{2}\right)+(\text { gof })\left(\frac{4}{3}\right)=1+1=2 \\$