Question

Need help with the composition of functions. I have attached a screenshot of the question.

Answer 1

using (f ○ g)(x) = f(g(x))

substitute x =
`(7)/(x)` into f(x)

f(
`(7)/(x)`) = 4 / (
`(7)/(x)` - 3 ) ×
`(x)/(x)`

=
`(4x)/(7-3x)`

The denominator of f(g(x)) cannot be zero as this would make f(g(x)) undefined. Equating the denominator to zero and solving gives the value that x cannot be

solve 7 - 3x = 0 ⇒ x =
`(7)/(3)`

domain : x ∈ ( - ∞,
`(7)/(3)`) ∪ (
`(7)/(3)`, + ∞ )