1. The problem asks to identify the inequality that represents the domain of the exponential piece of the function $f$, which is composed of an exponential piece and a polynomial piece. 2. From the description, the exponential piece is on the right side of $x \approx -1$, and the polynomial piece is on the left side. 3. The domain of the exponential piece is therefore all $x$ values greater than or equal to $-1$ because the pieces meet near $(-1,1)$. 4. The inequality representing this domain is $x \geq -1$. 5. Among the options, this corresponds to option C: $x \geq -1$. Final answer: C. $x \geq -1$