Dividing functions

Dividing functions

Lessons

Dividing functions: (fg)(x)=f(x)g(x)(\frac{f}{g})(x)=\frac{f(x)}{g(x)}
  • 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
    a)
    f(x)=3x8 f(x)=3x-8
    g(x)=x+2g(x)=x+2

    b)
    f(x)=4x3+5x2 f(x)=4x^3+5x^2
    g(x)=xg(x)=x

    c)
    f(x)=2x2+4x30 f(x)=2x^2+4x-30
    g(x)=2x6g(x)=2x-6

    d)
    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}
    a)
    state the domain of f(x) f(x)
    and g(x)g(x)

    b)
    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)

    c)
    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
    a)
    Determine the equation of the function
    h(x)=(gf)(x)h(x)=(\frac{g}{f})(x) and state the domain restrictions

    b)
    Sketch the graph of
    h(x)=(gf)(x)h(x)=(\frac{g}{f})(x)