The piecewise function $f(x)$ you've described is defined differently depending on the value of $x$. However, there seems to be a contradiction in the intervals provided:

1. $f(x) = x + 1$ if $x < 2$
2. $f(x) = x^2$ if $x \geq -1$

The issue is that the second condition $x \geq -1$ overlaps with the first condition $x < 2$. Therefore, we need to clarify how to define $f(x)$ for $-1 \leq x < 2$ where both conditions could apply.

One possible interpretation is to consider that the first condition takes priority for values of $x$ less than 2, and the second condition takes priority for values of $x$ greater than or equal to 2.

So, the piecewise function can be defined as:

\begin{cases} x + 1 & \text{if } x < 2 \\ x^2 & \text{if } x \geq 2 \end{cases}$$ This interpretation assumes that $$f(x) = x^2$$ only applies strictly when $$x \geq 2$$. If instead, you meant $$f(x) = x^2$$ to apply as soon as $$x \geq -1$$, you would need to define how the function behaves within the overlapping interval $$-1 \leq x < 2$$. Would you like to discuss this further or need clarification? ### Related Questions: 1. What is the value of $$f(x)$$ at $$x = 0$$? 2. How would you graph this piecewise function? 3. What is the value of $$f(x)$$ at $$x = 2$$? 4. Can you find the derivative of this piecewise function? 5. How does this piecewise function behave as $$x$$ approaches $$2$$? **Tip:** When dealing with piecewise functions, ensure the intervals do not overlap, or clearly define which condition applies within overlapping intervals.