SECTION $2\mathrm{.}1$ Functions

$61$

$59.h(x)=\sqrt[\phantom{2}]{3x-12}$

$60.G(x)=\sqrt[\phantom{2}]{1-x}$

$61.p(x)=\frac{x}{|2x+3|-1}$

$62.f(x)=\frac{x-1}{|3x-1|-4}$

$63.f(x)=\frac{x}{\sqrt[\phantom{2}]{x-4}}$

$64.f(x)=\frac{-x}{\sqrt[\phantom{2}]{-x-2}}$

$65.P(t)=\frac{\sqrt[\phantom{2}]{t-4}}{3t-21}$

$66.h(z)=\frac{\sqrt[\phantom{2}]{z+3}}{z-2}$

$67.f(x)=\sqrt[3]{5x-4}$

$68.g(t)=-t^2+\sqrt[3]{t^2+7t}$

$69.M(t)=\sqrt[5]{\frac{t+1}{t^2-5t-14}}$

$70.N(p)=\sqrt[5]{\frac{p}{2p^2-98}}$ In Problems $71-80,$ for the given functions $f$ and $g,$ find the following. For parts $($a$)-($d$),$ also find the domain.

$($a$)(f+g)(x)$

$($b$)(f-g)(x)$

$($c$)(f*g)(x)$

$($d$)(\frac{f}{g})(x)$

$($e$)(f+g)(3)$

$($f$)(f-g)(4)$

$($g$)(f*g)(2)$

$($h$)$

$(1)$

$71.f(x)=3x+4$;$,g(x)=2x-3$

$72.f(x)=2x+1$;$,g(x)=3x-2$

$73.f(x)=x-1$;$g(x)=2x^2$

$74.f(x)=2x^2+3$;$,g(x)=4x^3+1$

$75.f(x)=\sqrt[\phantom{2}]{x}$;$,g(x)=3x-5$

$76.f(x)=|x|$;$,g(x)=x$

$77.f(x)=1+\frac{1}{x}$;$,g(x)=\frac{1}{x}$

$78.f(x)=\sqrt[\phantom{2}]{x-1}$;$g(x)=\sqrt[\phantom{2}]{4-x}$

$79.f(x)=\frac{2x+3}{3x-2}$;$,g(x)=\frac{4x}{3x-2}$

$80.f(x)=\sqrt[\phantom{2}]{x+1}$;$,g(x)=\frac{2}{x}$