Question

can someone help me??? find functionsf and g so that f composite g =H... H(x)=1/(x^2-8)

Answer 1

\[g(x) = x^{2}-8, f(x) = \frac{1}{x}\]
thats one way to do it.

Answer 2

or:
\[g(x) = x^{2}, f(x) = \frac{1}{x-8}\]
that works too.

Answer 3

or if you wanna be cheap about it (this will work in every case):
\[g(x) = x, f(x) = \frac{1}{x^{2}-8}\]

Answer 4

how do u got that??? can u show me step by step???

Answer 5

sure, although its not something i can really show, its a bunch of explanation. So this is your problem:
\[\frac{1}{x^{2}-8}\]
First, i want to see what is the general form of this function. Its general form is:
\[\frac{1}{junk}\]
That is why i mae the outside function (f in your case):
\[f(x) = \frac{1}{x}\]

Answer 6

Second, i ask myself, "what is the junk?", well we can see that the junk is:
\[x^{2}-8\]
so thats what i made the inside function. g has to be:
\[g(x) = x^2-8\]

Answer 7

So following these two steps, could you tell me what two functions would form:
\[\frac{1}{x+5}\]
? its the exact same process.

Answer 8

1/x and x+5.. is that right?

Answer 9

yep, perfect :)

Answer 10

sometimes it might get a little more complicated. it just comes down to can you identify the junk.

Answer 11

ok... thnkas for helping..

Answer 12

hiihih ok

Answer 13

a slightly harder example:
\[(x+3)^{2} +5(x+3) -2\]
this is in the form:
\[(junk)^2+5(junk)-2\]
so my two functions would be:
\[f(x) = x^2+5x-2, g(x) = x+3\]

Answer 14

good job, medals for everyone lol