Find 1/f(x) for:

(a) f(x) = x^3 + 1

(b) f(x) = |x|

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- Jan 19th 2007, 01:13 PMsymmetryFind 1/f(x)
Find 1/f(x) for:

(a) f(x) = x^3 + 1

(b) f(x) = |x| - Jan 19th 2007, 01:41 PMtopsquark
- Jan 19th 2007, 01:51 PMAfterShock
This is a quite self-explanatory problem.

Perhaps the only thing that can be expanded upon is factoring x^3 + 1 to (x + 1)*(x^2 - x + 1), but like the -f(x) problem, this is something you should go back to the basics of what "f(x)" means if you don't understand this. - Jan 19th 2007, 06:35 PMsymmetryok
Thanks! In fact, we should go back to the basics.

Now, f(x) is read "f of x" Correct?

Just like so many students, we write f(x) all the time.

However, we do not have a clear view of f of x.

QUESTIONS:

(a) What exactly does f(x) really mean in math?

(b) Why does y = f(x) and vice-versa? - Jan 20th 2007, 12:39 AMCaptainBlack
A function is a mapping between elements in one set D (the domain) and

another set C (the range), such that for every x in D there is one and only

one y in C.

We write f:x to y, and often f(x)=y, here f is a name for the function.

When we write something like f(x)=x^2+1 in elementary maths we are taking

as read that D is the subset of the reals R, for which the term on the right

of the equals sign makes sense and gives but a single value. Also we are

taking it as read that the range is that part of R which is the image under f

of D. This identifies the number in C which f maps x onto.

Now if we have a function f(x) when we talk about 1/f(x) we mean the

function g(x) such that for any x in D (and f(x)!=0):

g(x)=1/f(x).

so if f(x) = x^3 + 1, we have:

g(x)=1/f(x)=1/(x^3+1)

RonL - Jan 20th 2007, 01:22 AMticbol
(a) What exactly does f(x) really mean in math?

f(x).

Here f is the function.

f(x) is the function when x is the, uh, what's the term here, input (?) or "thing" that the function f is "applied" onto.

f(3) is the function f "applied" on 3.

Say f is "the square of something minus 5"

If the something is x, then f(x) = x^2 -5

If the something is 3, then f(3) = 3^2 -5

---------------------------

(b) Why does y = f(x) and vice-versa?

y = f(x) because we are used to the x,y rectangular or Cartesian axes. If x represents the domain of the function, then how do you graph the range f(x)? There is no f(x) in the said rectangular axes. So, we let y represent f(x). Hence let y = f(x) so that we may visualize the graph of f(x) on the x,y axes.

If the axes were (x,z), then let z = f(x) so that we may visualize the graph of f(x) on the x,z axes.

Vice-versa?

Not strictly. y may not equal f(x) always. But in the assumption or supposition y = f(x), since the two are supposed to be equal to each other, then the vice-versa is true. - Jan 20th 2007, 05:40 AMsymmetryok
I have a great collection of notes for my exam.

Thanks!