```ts
export function mergeIntervals(intervals: number[][]):[number[]] {
  if (intervals.some(([start, end]) => start > end)) {
    throw new Error("Invalid interval: start is greater than end");
  }

  intervals.sort((a, b) => a[0] - b[0]);

  const mergedIntervals = [intervals[0]];

  for (let i = 1; i < intervals.length; i++) {
    const lastInterval = mergedIntervals[mergedIntervals.length - 1];
    if (lastInterval[1] >= intervals[i][0]) {
      // Merge or extend the last interval
      lastInterval[1] = Math.max(lastInterval[1], intervals[i][1]);
    } else {
      // Add a new interval
      mergedIntervals.push(intervals[i]);
    }
  }

  return mergedIntervals;
}
```