Name: Majeedah
Who is asking: Student
Level of the question: Secondary

Question: I'm upgrading thru correspondence and haven't been in school for a long while, so I have no class or teacher to explain the basics to me.

I have a couple of questions:

The problem is this:

  1. f(x) = x2 - 2, Find the expression.

    Q f(-x)
    A x2 - 2

    Why is the answer not -x2 - 2?

  2. A relation f, is given by f(x) = x - 2/x. Find the expression.

    Q 2/f(3)
    A 6

    How do you get the answer.

 

Majeedah,

  1. What this means is you need to substitute "-x" for all values of "x"
    in the expression:

    f(-x) = (-x)2 - 2
    but since (-x)2 = (-x) (-x) and the product of two negative numbers is positive,
    (-x)2 = x2. By convention, when we simplify this expression we drop the minus sign because it is simpler to write x2 than (-x)2. Hence f(-x) = x2 - 2.

    Writing -x2 - 2 is not the same as (-x)2 -2 because the order of operations (look up "BEDMAS" in our search form for more information on this) says that the x2 must be evaluated before the minus. For
    example, if x is 2, then
    -22 - 2 = - 2 2 - 2 = -4 - 2 = -6, but (-2)2 - 2 = (-2) (-2) - 2 = 4 - 2 = 2.

  2. Replace x with 3 to find f(3):
    f(3) = 3 - 2/3.
    Put that under 2 to find 2/f(3):
    2/f(c) = 2 / (3- 2/3)
    Now you simplify the left-hand side to get the answer:
    2 / (3 - 2/3) = 2 / (7/3) = 2 (3/7) = 6/7
    Clearly the answer is not 6, but 6/7.

    I'm guessing that you forgot some parentheses. If f(x) = (x-2) / x then
    f(3) = (3-2) / 3 = 1/3
    and so
    2 / f(3) = 2 / (1/3) = 2 (3/1) = 6.

     

Hope this helps,
Stephen La Rocque.