Answer:
[tex](f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10[/tex]
Step-by-step explanation:
The given functions are:
[tex]f(x) = {x}^{3} - 2 {x}^{2} + 12x - 6[/tex]
and
[tex]g(x) = 4 {x}^{2} - 6x + 4[/tex]
We want to find
[tex](f - g)(x)[/tex]
Recall that:
[tex](f - g)(x) = f(x) - g(x)[/tex]
This implies that:
[tex](f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - (4 {x}^{2} - 6x + 4)[/tex]
[tex](f - g)(x) = {x}^{3} - 2 {x}^{2} + 12x - 6 - 4 {x}^{2} + 6x - 4[/tex]
We combine similar terms to get:
[tex](f - g)(x) = {x}^{3} - 6 {x}^{2} + 18x - 10[/tex]
