Explanation:

The Tungabhadra Doab, the region between the Tungabhadra and Krishna rivers, has been historically significant for various empires and dynasties due to its fertile lands and strategic location. Here's a brief historical context about the mentioned dynasties:

Western Chalukyas: The Western Chalukya Empire was an important Indian dynasty that ruled most of the western Deccan, South India, between the 10th and 12th centuries. The region of the Tungabhadra Doab came under their influence, and they had frequent conflicts with other dynasties like the Cholas over the control of this region.

Hoysalas: The Hoysalas emerged as a powerful dynasty in the 12th and 13th centuries, with their capital at Halebidu in modern Karnataka. They too had an interest in the Tungabhadra Doab, especially during the times they expanded northwards.

Rashtrakutas: The Rashtrakuta Dynasty ruled large portions of the Indian subcontinent between the 6th and the 10th century. During their reign, they controlled vast territories in the Deccan region, which included the Tungabhadra Doab.

Considering the influence and control of these dynasties over the Tungabhadra Doab at different points in history, all three (Western Chalukyas, Hoysalas, and Rashtrakutas) had associations with this region.