Question

Someone help please.

Answer 1

Given f(x)=x^2+7 and g(x)=x-4/x. Find (g (of) f)(-1)

Answer 2

A composite function, is the combination of two functions in order to create a third which has the combined features of the first two.
The notation \((gof)(x)\) means \(g(f(x))\) which in essence, we could translate to "f composite in g".

Now, when you write the composite function of other two, the whole composition of the first one will be composing the "x"s of the second, that'll create a new function which is the very composition and combination of the two desired.
so, having:
\[f(x)=x^2+7\]
\[g(x)=\frac{ x-4 }{ x }\]
The composite function gof will be taking the function f(x) and writing it instead of the x's on the function g(x):
\[(gof)(x)=\frac{ (x^2+7)-4 }{ x^2+7 }\]

Answer 3

Is that how you find (go f)(f-1)?

Answer 4

no, right now, you have found the general form of the composite function, if you want to find (gof)(-1) you replace the "x" for -1 and do the operations.

Answer 5

Can you show me an example of how to do the operations?

Answer 6

for example:
\[(gof)(x)=x^2-2x\]
if I want to find (gof)(-1) I would write it like this:
\[(gof)(-1)=(-1)^2-2(-1)\]
Therefore, the result would be:
\[(gof)(-1)=3\]

Answer 7

(go f)(-1)=(-1+7)-4/ -1^2+7
Something like that?

Answer 8

yes

Answer 9

Ahhh, so, is that my answer?

Answer 10

yes, that can work out.

Answer 11

Thanks!