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About LinkBacksFind 1/f(x) for:
(a) f(x) = x^3 + 1
(b) f(x) = |x|
This is a quite self-explanatory problem.Originally Posted by topsquark
Not to sound insulting, but c'mon!
a)
b)
-Dan
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.
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?
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
(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
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(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.
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