Chapter 9 - Section 9.1 - The Algebra of Functions; Composite Functions - Exercise Set - Page 540: 7

$(f+g)(x)=5x^2-3x$ $(f−g)(x)=-5x^2-3x$ $(f×g)(x)=-15x^3$ $(\frac{f}{g})(x)=\frac{-3}{5x}$

If $f(x)=-3x$ and $g(x)=5x^2$, then $(f+g)(x)=f(x)+g(x)=-3x+5x^2=5x^2-3x$ $(f−g)(x)=f(x)−g(x)=-3x-5x^2=-5x^2-3x$ $(f×g)(x)=f(x)×g(x)=(-3x)\times(5x^2)=-15x^3$ $(\frac{f}{g})(x)=\frac{f(x)}{g(x)}=\frac{-3x}{5x^2}=\frac{-3}{5x}$