As an example. let "f" be a function which doubles a number (multiplies it by 2), and let "g" be a function which subtracts 1 from a number. These two functions can be written as:
Here, "g" composed with "f" would be the function which doubles a number, and "then" subtracts 1 from it. That is:
On the other hand, "f" composed with "g" would be the function which subtracts 1 from a number, and "then" doubles it:
Composition of functions can also be generalized to binary relations, where it is sometimes represented using the same formula_5 symbol (as in formula_6).
Function composition can be proven to be associative, which means that:
However, function composition is in general not commutative, which means that:
This can be also seen in the first example, where "(g ∘ f)(2) = 2*2 - 1 = 3" and "(f ∘ g)(2) = 2*(2-1) = 2".
Double
Double may mean:
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Rene Kulitja (born 1958), also known as Wanuny Kulitja, is an Aboriginal Australian artist. She works with a range of media, including paint, glass and ceramics. Her most famous design is probably "Yananyi Dreaming", which covers a Qantas Boeing 737.
Rene was born in 1958, in Ernabella, South Australia. Her family are Pitjantjatjara people, and her Pitjantjatjara name is Wanuny. She grew up in northern South Australia, and then moved to Docker River after she got married. When Uluṟu-Kata Tjuṯa National Park was handed back to traditional owners in 1985, the couple moved to Muṯitjulu to work in tourism. Rene became involved in arts and crafts at the women's centre shortly after. She was a founding director of Walkatjara Art.
During the mid-1990s, Kulitja worked with other women artists on the interior design of the park's cultural centre. She also took a course on glasswork techniques at the University of South Australia, along with three other women. After a successful exhibition of work made using these new skills, Kulitja and the other women got a commission from the Ayers Rock Resort at Yulara for a panel of glass decorated with traditional designs.
In 2000, Kulitja was one of over 300 Aboriginal women from Central Australia to perform at the Opening Ceremony of the Summer Olympic Games in Sydney.
In 2002, Kulitja worked with Balarinji Studio in Sydney to design the outside surface of Qantas Boeing 737. The design she painted was of Uluṟu. It was based on traditional designs and sacred Dreaming legends. The fleet was launched on 14 February 2002, with a special ceremony performed by singers and dancers from Muṯitjulu. The word "(y)" means "to go" or "to travel" in Pitjantjatjara and Yankunytjatjara. It was the third Qantas aircraft to be painted in an Aboriginal design. Kulitja did something similar again in 2010, when a semi-trailer truck was decorated with another of her designs as part of a national roadshow by Maṟuku Arts.
Kulitja has held an important position within her community for several years. She has been a member of both the Muṯitjulu Community Council and the Board of Management of Uluṟu-Kata Tjuṯa National Park. In 2006, she became the chairperson of Maṟuku Arts. In October 2007, she was elected for a two-year term as a director on the Ngaanyatjarra, Pitjantjatjara and Yankunytjatjara (NPY) Women's Council.
Rene's husband, Richard Kulitja, worked in the tourist industry for many years. In 2004, he accepted an international tourism award in Washington, D.C. on behalf of Aṉangu Tours. Several members of their family have been badly affected by petrol sniffing, which is a widespread problem amongst Aboriginal communities in central Australia. Their son was addicted to sniffing, and was reported to be getting help in 2006. Rene's two brothers also have permanent brain damage caused by their past addictions to the substance. Rene has spoken strongly about addressing the issue within the community.
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