Question

If `f ( x ) = \frac { x - 3} { x }` and `g(x) = 5x-4`, what is the domain of `(f*g)(x)`?

Answer 1

`{x inR| x!=4/5}`

Explanation:

First figure out what `(f*g)(x)` is to do this just put the `g(x)` function into both of the x spots in `f(x)`

`(f*g)(x)=(5x-4-3)/(5x-4)` so `(f*g)(x)=(5x-7)/(5x-4)`

We note that for a rational function basically `1/x` when the denominator is equal to 0 there is no output

So we have to figure out when `5x-4=0`

`5x=4` so `x=4/5`

So the domain is all the reals apart from `x=4/5`
`{x inR| x!=4/5}`