Question 11

Explanation

We are asked to find the interval of $x$ values where the function value $f(x)$ is greater than or equal to $5$ ($f(x) \geq 5$).

Let's check each part of the function one by one:

1. Interval $0 \leq x < 2$

   In this interval, $f(x) = 3$. Is $3 \geq 5$? No. So, this interval does not satisfy the condition.

2. Interval $2 \leq x < 5$

   In this interval, $f(x) = 5$. Is $5 \geq 5$? Yes. So, the interval $[2, 5)$ satisfies the condition.

3. Interval $5 \leq x < 8$

   In this interval, $f(x) = 7$. Is $7 \geq 5$? Yes. So, the interval $[5, 8)$ satisfies the condition.

4. Interval $8 \leq x < 10$

   In this interval, $f(x) = 9$. Is $9 \geq 5$? Yes. So, the interval $[8, 10)$ satisfies the condition.

Combining Intervals

We combine all intervals that satisfy the condition:

Note that the right end of the first interval ($5$) matches the left end of the second interval, and the right end of the second interval ($8$) matches the left end of the third interval. Since the connection is continuous (closed at the start, open at the end, then closed again at the next start), we can merge them into a single continuous interval.

Thus, the interval of $x$ values that satisfies the condition is $x \in [2, 10)$.