1. ## Functions!

If f(x) = (1-x)
------
x
what is f(f(x))

please could you explain it too? I have no idea whatsoever what I'm doing.

2. Originally Posted by Anna-Banannna!
If f(x) = (1-x)
------
x
what is f(f(x))

please could you explain it too? I have no idea whatsoever what I'm doing.
here is how function notations work. whatever shows up in the brackets, you replace x with it (or whatever variable the function is defined for)

example: if $\displaystyle g(x) = x^2 + 2x + 3$

then, $\displaystyle g(1) = (1)^2 + 2(1) + 3 = 6$ ..........i replaced x with 1

$\displaystyle g(3) = (3)^2 + 2(3) + 3 =$ ..................i replaced x with 3

$\displaystyle g($ $\displaystyle ) = ($ $\displaystyle )^2 + 2($ $\displaystyle ) + 3$ ...............i replaced x with ....(assume is in the domain of g(x) )

what if we had another function?

$\displaystyle h(x) = x + 1$

then, $\displaystyle g(h(x)) = (h(x))^2 + 2(h(x)) + 3 = (x + 1)^2 + 2(x + 1) + 3$ ...........i replaced the x in g(x) with h(x)

and

$\displaystyle h(g(x)) = (g(x)) + 1 = (x^2 + 2x + 3) + 1 = x^2 + 2x + 4$ ............i replaced the x in h(x) with g(x)

now, can you do your problem?

3. thanks, I understand the ones you did, but all the divisions are confusing me. I have the top line as 1- (1-x/x) and my dad gave me the bottom line as 1-(x/x) but I don't get that bit either.

Sorry, maths is NOT my best subject.

4. Originally Posted by Anna-Banannna!
thanks, I understand the ones you did, but all the divisions are confusing me. I have the top line as 1- (1-x/x) and my dad gave me the bottom line as 1-(x/x) but I don't get that bit either.

Sorry, maths is NOT my best subject.
the divisions don't matter. the same rule applies. wherever you see x in your function, replace it with f(x), then just write out what f(x) is, just as i did with my last two examples

try again

5. Um... 1- ((1-x)/x)/x)?

6. Wait I get it!!!! Does 1= x/x?

7. Originally Posted by Anna-Banannna!
Um... 1- ((1-x)/x)/x)?
ok, i am not sure what you wrote. was the original function $\displaystyle f(x) = \frac {1 - x}x$?

in that case, the first step would be: $\displaystyle f(f(x)) = \frac {1 - (f(x))}{(f(x))}$

now what would it be?

9. Originally Posted by Anna-Banannna!
Wait I get it!!!! Does 1= x/x?
yes, 1 = x/x

but you don't have the right answer anyway, the thing you typed seems wrong--if i interpreted your question correctly

10. Originally Posted by Anna-Banannna!