Answer
(a) $f(x) + g(x) = 4x - 6$
Domain: {$x|x$}
(b) $f(x) - g(x) = 2x + 4$
Domain: {$x|x$}
(c) $f\times g = 3x^{2} -16x + 5$
Domain: {$x|x$}
(d) $\frac{f}{g} = \frac{3x - 1}{x-5}$
Domain: {$x| x\ne 5$}
Work Step by Step
a) $f + g$
$f(x) + g(x) = (3x - 1) + (x - 5)$
$f(x) + g(x) = 3x - 1 + x - 5$
$f(x) + g(x) = 4x - 6$
Domain: {$x|x$} because variables in polynomial functions include all Real numbers.
b) $f - g$
$f(x) - g(x) = (3x - 1) - (x - 5)$
$f(x) - g(x) = 3x - 1 - x + 5$
$f(x) - g(x) = 2x + 4$
Domain: {$x|x$} because variables in polynomial functions include all Real numbers.
c) $fg$
$f\times g = (3x - 1)(x-5)$
$f\times g = 3x^{2} - 15x - 1x +5$
$f\times g = 3x^{2} -16x + 5$
Domain: {$x|x$} because variables in polynomial functions include all Real numbers.
d) $\frac{f}{g}$
$\frac{f}{g} = \frac{3x - 1}{x-5}$
Domain: {$x| x\ne 5$} since rational functions cannot include values that make the denominator = $0$:
**$x - 5 \ne 0$
**$x \ne 0 + 5 = 5$
