Given:
[tex]\begin{gathered} f(x)=3x^2+6x-5 \\ g(x)=4x^3-5x^2+6 \end{gathered}[/tex]
Then, (f+g)(x) is:
[tex]\left(f+g\right)\left(x\right)=f(x)+g(x)[/tex]
Substitute the equations:
[tex](f+g)(x)=3x^2+6x-5+4x^3-5x^2+6[/tex]
Grouping similar terms:
[tex]4x^3+3x^2-5x^2+6x-5+6[/tex]
Simplify:
[tex]4x^3-2x^2+6x+1[/tex]
Answer: C.
[tex](f+g)(x)=4x^3-2x^2+6x+1[/tex]
