Chapter 4, Exponential and Logarithmic Functions - Chapter 4 Review - Concept Check - Page 425: 18

Domain: $-1\lt x\lt2$

We must have that: $2+x-x^2\gt0$ $2+2x-x-x^2\gt0$ $2(1+x)-x(1+x)\gt0$ $(2-x)(1+x)\gt0$ Both factors must be positive: $2-x\gt0$ $-x\gt-2$ $x\lt2$ $1+x\gt0$ $x\gt-1$ $-1\lt x\lt2$ Or both factors must be negative: $2-x\lt0$ $-x\lt-2$ $x\gt2$ $1+x\lt0$ $x\lt-1$ A number can not be greater than 2 and less than -1 at the same time.