Answer
The answers are
$ (f+g)(x) = 3x-3 $
$ (f-g)(x)=7x+3 $
$ (fg)(x)= -10x^2-15x $
$ \left (\frac{f}{g} \right )(x) = \frac {5x}{-2x-3} $
Work Step by Step
Given functions are
$ f(x)=5x $ and $ g(x)=-2x-3 $
$ (f+g)(x) = f(x)+g(x) $
Substitute values.
$ (f+g)(x) = 5x-2x-3 $
$ (f+g)(x) = 3x-3 $
$ (f-g)(x) = f(x)-g(x) $
Substitute values.
$ (f-g)(x)=5x-(-2x-3) $
$ (f-g)(x)=5x+2x+3 $
$ (f-g)(x)=7x+3 $
$ (fg)(x)=f(x)\times g(x) $
Substitute values.
$ (fg)(x)=(5x) \times (-2x-3) $
$ (fg)(x)= -10x^2-15x $
$ \left (\frac{f}{g} \right )(x) = \frac {f(x)}{g(x)} $
Substitute values.
$ \left (\frac{f}{g} \right )(x) = \frac {5x}{-2x-3} $ .