# A monotonically decreasing function and inequality

Can it be shown that when $$\mathbb{R}_0^+\colon=[0,\infty[$$ for all $$x\ge0$$ that $$\ln(x+1)\le x$$ so far I have shown $$f{'}(x)= \frac{1}{1+x}-1<0$$ hence function is monotonically decreasing and has a global maximum at $$x=0$$

$f(x) \leq f(0) \to \ln(1+x) - x \leq 0 \to \ln(1+x) \leq x$.