Functions

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Functions:

Determining the range of a function:

The range of a function can simply be found by putting the numbers into the function.

I.E:

Find the range of f(x) = 3x + 5 (http://www.bbc.co.uk/staticarchive/8dd0578c3f5275766d326fd5bfb68fa74956a424.gif) for domain {1,2,3} (http://www.bbc.co.uk/staticarchive/7a0378f59092037a02575c2ff9b6af21bc2b2360.gif)

  • f(1) = 3(1) + 5 = 8 (http://www.bbc.co.uk/staticarchive/934cd960ffc3247682d34051c46c392bf1bcba81.gif)
  • f(2) = 3(2) + 5 = 11 (http://www.bbc.co.uk/staticarchive/21d8965c7bbfaf7390e8ce287d92ac6b5c1a6115.gif)
  • f(3) = 3(3) + 5 = 14 (http://www.bbc.co.uk/staticarchive/0d598d9bf80d675f0c21340ee8bb171a0456b183.gif)

Range of f(x) = {8, 11, 14} (http://www.bbc.co.uk/staticarchive/4ff009f7f916127ea57a62575e90161e2623be1b.gif)

Composite functions:

Composite functions are when 2 functions are combined together. This is achieved by putting one of the functions within the other.

  • f ( x ) = 10x +7 (http://www.bbc.co.uk/staticarchive/e53cf1e8f7a7ecdca6662941a401119ecb14c4a9.gif)
  • g ( x ) = 3x (http://www.bbc.co.uk/staticarchive/9c75ad9482ce84d6a878b7f3d14f440a2771e451.gif)
  • Find f ( g ( x ) ) (http://www.bbc.co.uk/staticarchive/8de3f9b76778d981efc03f97d8367a33fc6b1de7.gif)
  • Replace x (http://www.bbc.co.uk/staticarchive/20680cb107766b2e03c23e79daa552b5e1881e05.gif) with the function
  • f ( g ( x ) ) = 10 ( g ( x ) ) + 7 (http://www.bbc.co.uk/staticarchive/69dec3020be21f6c0fa0d4d32575f1a32ca78a67.gif)
  • f ( 3x ) = 10 ( 3x ) + 7 (http://www.bbc.co.uk/staticarchive/5f8662ff4ff9119fd317b309b98002aae2da4c5b.gif)
  • f ( g ( x ) ) = 30x + 7 (http://www.bbc.co.uk/staticarchive/8d3f5a8d563972f2738bdbde8ba74f6b8cb6b094.gif)

Inverse functions:

To find the inverse of a…

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