Subtracting functions

Subtracting functions

Lessons

subtracting functions: (fg)(x)=f(x)g(x)(f-g)(x) = f(x)-g(x)
  • 1.
    Determine the Difference of Two Functions Algebraically
    If f(x)=5x3x+6f(x)= 5x^3-x+6
    and
    g(x)=4x8,g(x)=4x-8,
    Determine:
    a)
    (fg)(x)(f-g)(x)

    b)
    (gf)(x) (g-f)(x)

    c)
    (gf)(2) (g-f)(-2)
    evaluate in two different ways


  • 2.
    Determine the Difference of Two Functions Graphically
    Given the graphs of functions f(x)f(x)
    and g(x)g(x)

    Subtraction of functions
    a)
    sketch: (gf)(x)(g-f)(x)

    b)
    evaluate:
    i)
    (gf)(3)(g-f)(-3)
    ii)
    (gf)(0)(g-f)(0)
    iii) (gf)(4)(g-f)(4)


  • 3.
    Determine the Difference of Two Functions Point-by-Point
    The graph of y=f(x)y=f(x)
    includes the points (2,5),(4,15),(7,30)
    The graph of y=g(x)y=g(x)
    includes the points (2,6),(3,16),(4,30)
    If f and g are defined for all real values of x , then which of the
    following points must lie on the graph of y=(fg)(x)?y=(f-g)(x)?
    a)
    (0,1) (0,-1)

    b)
    (0,1) (0,1)

    c)
    (2,1) (2,-1)

    d)
    (3,30) (3,30)