Answer:
[tex](f-g)(x)=x^{4}-x^{3}+2x-6[/tex]
Step-by-step explanation:
1- You have the following fucntion given in the problem:
[tex]f(x)=x^{4}-3x^{2}+5x-7\\g(x)=x^{3}-3x^{2}+3x-1[/tex]
2. To solve this exercise you only need to subtract [tex]f(x)[/tex] and [tex]g(x)[/tex], as following:
- Multiply signs.
- Add the like terms.
Then:
[tex](f-g)(x)=(x^{4}-3x^{2}+5x-7)-(x^{3}-3x^{2}+3x-1)\\(f-g)(x)=x^{4}-3x^{2}+5x-7-x^{3}+3x^{2}-3x+1\\(f-g)(x)=x^{4}-x^{3}+2x-6[/tex]
