Answer
(a) $x \in (-1,0)$
(b) $x \in (0,1)$
(c) $x \in (-\infty,-1)$
(d) $x \in (1,\infty)$
Work Step by Step
The function value is decreasing when $x$ is positive and is increasing when $x$ is negative. The rate of change is becoming more negative in the range $0 \lt x \lt 1$, so it is concave down in that range. The rate of change is becoming less negative in the range $1 \lt x \lt \infty$, so it is concave up in that range. The rate of change is becoming less positive in the range $-1 \lt x \lt 0$, so it is concave down in that range. The rate of change is becoming more positive in the range $-\infty \lt x \lt -1$, so it is concave up in that range.
