It was thus a natural choice for that seat's one-term Liberal member, Don Dobie, to transfer after the creation of Cook erased his majority in Hughes.

In 2006, the Australian Electoral Commission's Redistribution Committee for New South Wales proposed that the division be jointly named for Joseph Cook, Prime Minister of Australia from 1913 to 1914, but this did not eventuate at the time.

[1] In 2024, the namesake was finally altered to be joint between both men, to give recognition to Joseph Cook and have a division named after him like other former Prime Ministers.

The most prominent members were Dobie, who held the seat from its 1969 creation until his retirement in 1996 (with a brief break from 1972 to 1975); Bruce Baird, a former Deputy Leader of the Liberal Party of New South Wales before his move into Federal politics; and Scott Morrison MP, former Prime Minister of Australia 2018–2022.

In 2007, following news of Baird's impending retirement, the seat attracted significant media attention, thanks to the controversial preselection of Liberal candidate Michael Towke.