Question

If f(x)=x-3/x and g(x)=5x-4, what is the domain of (f•g)(x)?

Answer 1

⅘ ≠ x → Set-Builder Notation

(-∞, ⅘) ∪ (⅘, ∞) → Interval Notation

Explanation:

Plug the g(x) function into the f(x) function for every x you see.

Answer 2

domain is the set of all real numbers except 0

Explanation:

If f(x)=x-3/x and g(x)=5x-4

(f•g)(x) is f(x) times g(x)

multiply f(x) and g(x)

(f•g)(x) is f(x) times g(x)

Replace f(x) and g(x)

`f(x) \cdot g(x)= (x-(3)/(x))(5x-4)`

Apply FOIL method to multiply it

multiply x inside the parenthesis

`5x^2-4x`

Multiply the fraction inside the parenthesis

`-5 +(12)/(x)`

`5x^2-4x -5 +(12)/(x)`

We have x in the denominator . Domain is the set of x value for which the function is defined.

When denominator x is 0 then the function is undefined

So domain is the set of all real numbers except 0