Question

The set of all x for which $\log (1+x)\le x$ is equal to $(-1,\infty ).$
True or False ? true=5 False=8

Answer 1

Given inequality $\log (1+x)\le x$
For above inequality to be defined,

$1+x\ge 0$

$\Rightarrow x\ge -1$

Since $\log x\le 0$ for all $xϵ(0,1)$ and $\log x\le x$ for all $xϵ(1,\infty )$
Hence,$x\ge -1$.
The solution set is $(-1,\infty )$.