Dividing functions

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Examples
Lessons
  1. Determine the Quotient of Two Functions and State Its Domain
    Write an expression in the simplest form for (fg)(x)(\frac{f}{g})(x)
    State the domain restrictions
    1. f(x)=3x8 f(x)=3x-8
      g(x)=x+2g(x)=x+2
    2. f(x)=4x3+5x2 f(x)=4x^3+5x^2
      g(x)=xg(x)=x
    3. f(x)=2x2+4x30 f(x)=2x^2+4x-30
      g(x)=2x6g(x)=2x-6
    4. f(x)=x3f(x)=x-3
      g(x)=x2+2x15g(x)=x^2+2x-15
  2. Operations of Functions – In a Nutshell
    Consider the functions f(x)=xx+5f(x)=\frac{x}{x+5}
    and g(x)=3xx2g(x)=\frac{3x}{x-2}
    1. state the domain of f(x) f(x)
      and g(x)g(x)
    2. write an expression in the simplest form for each
      of the following and state the domains
      i) (f+g)(x)(f+g)(x)
      ii) (fg)(x)(f-g)(x)
      iii) (fg)(x)(fg)(x)
      iv) (fg)(x)(\frac{f}{g})(x)
    3. evaluate (fg)(4)(\frac{f}{g})(4)
      in 2 different ways
  3. Sketch the Quotient of Two Functions
    Consider the functions f(x)=2x2+4x30f(x)=2x^2+4x-30
    g(x)=20x60g(x)=20x-60
    1. Determine the equation of the function
      h(x)=(gf)(x)h(x)=(\frac{g}{f})(x) and state the domain restrictions
    2. Sketch the graph of
      h(x)=(gf)(x)h(x)=(\frac{g}{f})(x)
Topic Notes
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Dividing functions: (fg)(x)=f(x)g(x)(\frac{f}{g})(x)=\frac{f(x)}{g(x)}