

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:

f(x) = x^{2}  2, Find the expression.
Q f(x)
A x^{2}  2
Why is the answer not x^{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,

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} = x^{2}. By convention, when we simplify this expression we drop the minus sign because it is simpler to write x^{2} than (x)^{2}. Hence f(x) = x^{2}  2.
Writing x^{2}  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 x^{2} must be evaluated before the minus. For
example, if x is 2, then
2^{2}  2 =  2 2  2 = 4  2 = 6, but (2)^{2}  2 = (2) (2)  2 = 4  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 lefthand 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) = (x2) / x then
f(3) = (32) / 3 = 1/3
and so
2 / f(3) = 2 / (1/3) = 2 (3/1) = 6.
Hope this helps,
Stephen La Rocque.



