Question

Use f(x)=5-x and g(x)=1/x-2 to find the following and identify its domain

Answer 1

Explanation:

f(x) = 5 - x

g(x) =
`(1)/(x-2)` (x ≠ 2)

(a). f(g(x)) = 5 -
`(1)/(x-2)`

f(g(x)) =
`(5x-11)/(x-2)`

Domain: x ≠ 2 or ( - ∞ , 2 ) ∪ ( 2 , ∞ )

(b). g(f(x)) =
`(1)/(3-x)`

Domain: x ≠ 3 or ( - ∞ , 3 ) ∪ ( 3 , ∞ )