Answer:
Explanation
The expression
[tex](f-g)(x)[/tex]is just another way of writing
[tex]f(x)-g(x)[/tex]Now,
[tex]f(x)=3x^5+6x^2-5[/tex][tex]g\mleft(x\mright)=3x^5-5x^4+3x^2-15[/tex]Therefore,
[tex]f(x)-g(x)=3x^5+6x^2-5-\lbrack3x^5-5x^4+3x^2-15\rbrack[/tex]expanding the expression in the brackets ( which involves expanding the negative sign) gives
[tex]f(x)-g(x)=3x^5+6x^2-5-3x^5+5x^4-3x^2+15\rbrack[/tex]combining the like terms gives
[tex]f(x)-g(x)=(3x^5-3x^5)+(6x^2-3x^2)+(-5+15)+5x^4[/tex][tex]=3x^2+10+5x^4[/tex]Hence,
[tex]\boxed{f\mleft(x\mright)-g\mleft(x\mright)=5x^4+3x^2+10.}[/tex]which is our answer!
