Answer :
To find and simplify f(x) - g(x), we subtract the function g(x) from f(x) and simplify the resulting expression. Therefore, f(x) - g(x) simplifies to [tex]-x^8 + 7x^3 + 3x^2 - 11.[/tex]
[tex]f(x) - g(x) = (-7x^9 - x^8 + 4x^3 - 6) - (-7x^9 - 3x^3 - 3x^2 + 5)[/tex]
When subtracting, we distribute the negative sign to each term in g(x):
[tex]f(x) - g(x) = -7x^9 - x^8 + 4x^3 - 6 + 7x^9 + 3x^3 + 3x^2 - 5[/tex]
Combining like terms:
[tex]f(x) - g(x) = -7x^9 + 7x^9 - x^8 + 4x^3 + 3x^3 + 3x^2 - 6 - 5[/tex]
The terms [tex]-7x^9 and 7x^9[/tex] cancel each other out:
[tex]f(x) - g(x) = 0 - x^8 + 7x^3 + 3x^2 - 6 - 5[/tex]
Simplifying further:
[tex]f(x) - g(x) = -x^8 + 7x^3 + 3x^2 - 11[/tex]
Learn more about expression: https://brainly.com/question/30265549
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