Question

If f(x)=x^2-2 and g(x)=x-3, what is (f*g)(x)?

Answer 1

This is a composite that could also be written in the form f(g(x)). Take the function defined as g(x) and stick it in in place of the x in f(x). Like this:
`f(g(x))=(x-3) ^(2) -2`. And that's it.

Answer 2

For this case we have the following functions:

`f (x) = x ^ 2 - 2 g (x) = x - 3`
We must make the following composition of functions:

`(fog) (x)`
This composition of functions means that we must replace the function g (x) in the function f (x) in the following way:

`f (g (x))`
We have then:

`f (g (x)) = (x - 3) ^ 2 - 2`
Rewriting we have:

`f (g (x)) = x ^ 2 - 6x + 9 - 2 f (g (x)) = x ^ 2 - 6x + 7`
Answer:

`f (g (x)) = x ^ 2 - 6x + 7`
option 2