Let $\text{⨍ }$ and g be increasing and decreasing functions respectively from $[0, \infty )$ to $[0,\infty )$ Let $h\left(x\right)=\text{⨍}$$\left(\mathrm{g}\right(\mathrm{x}).$ If $\mathrm{h}\left(0\right)=0,$ then $\mathrm{h}\left(\mathrm{x}\right)-\mathrm{h}\left(1\right)$ is

given

${\text{⨍ }}^1{\text{(x)<0, g}}^{\text{1}}\text{(x)<0}$

for $\mathrm{x}\ge 0$

$$\begin{gathered} \text{⨍ x, g(x)≥0} \\ \mathrm{h}\left(\mathrm{x}\right)=\text{⨍ (g(x))≥0 - ①} \\ {\mathrm{h}}^1\left(\mathrm{x}\right)={\text{⨍ }}^1{\text{(g(x)).g}}^1\text{(x)<0} \\ \mathrm{x}\ge 0 \\ \mathrm{h}\left(\mathrm{x}\right)\le 0 - ② \end{gathered}$$

from eq $①$ & eq $②$

$$\begin{gathered} \mathrm{h}\left(\mathrm{x}\right)=0 \\ \mathrm{h}\left(1\right)=0 \\ \mathrm{h}\left(\mathrm{x}\right)-\mathrm{h}\left(1\right)=0 \end{gathered}$$