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Functions, EXT1′ F1 2017 HSC 8 MC

Suppose that  `f(x)`  is a non-zero odd function.

Which of the functions below is also odd?

  1. `f(x^2)cosx`
  2. `f(f(x))`
  3. `f(x^3)sinx`
  4. `f(x^2) - f(x)`
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`B`

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`text(By trial and error, consider)\ B:`

`f(f(−x))` `= f(−f(x))`
  `= −f(f(x))`

 
`:. f(f(x))\ text(is odd.)`

`=> B`

Functions, EXT1′ F1 2012 HSC 11f

Sketch the following graphs, showing the `x`- and `y`-intercepts

  1.  `y = |\ x\ |- 1`   (1 mark)
  2.  `y = x(|\ x\ | - 1)`    (2 marks)

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  1. `text(See Worked Solutions.)`
  2. `text(See Worked Solutions.)`
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i. & ii.  

Graphs, EXT2 2012 HSC 11f Answer

`text{Note for part (ii)}`

`=>y = x(|\ x\ | – 1)\ \ text(is an ODD function)`