For this case we have the following functions:
[tex]f (x) = x ^ 2-6x\\g (x) = x ^ 3[/tex]
We must find [tex](f_ {0} g) (x):[/tex]
By definition of composition of functions we have to:
[tex](f_ {0} g) (x) = f (g (x))[/tex]
So:
[tex](f_ {0} g) (x) = (x ^ 3) ^ 2-6 (x ^ 3) = x ^ 6-6x ^ 3[/tex]
Recall that by definition of power properties is met:
[tex](a ^ n) ^ m = a ^ {n * m}[/tex]
Answer:
[tex](f_ {0} g) (x) = x ^ 6-6x ^ 3[/tex]
