91Ó°ÊÓ

Find the variation constant and an equation of variation for the given situation. \(y\) varies inversely as \(x,\) and \(y=\frac{1}{5}\) when \(x=35\).

Given that \(f(x)=3 x+1, g(x)=x^{2}-2 x-6,\) and \(h(x)=x^{3},\) find each of the following. $$(g \circ g)(3)$$

Given that \(f(x)=x^{2}-3\) and \(g(x)=2 x+1,\) find each of the following, if it exists. $$(g / f)\left(-\frac{1}{2}\right)$$

First, graph the equation and determine visually whether it is symmetric with respect to the \(x\) -axis, the \(y\) -axis, and the origin. Then verify your assertion algebraically. $$2 x-5=3 y$$

Find the variation constant and an equation of variation for the given situation. \(y\) varies inversely as \(x,\) and \(y=1.8\) when \(x=0.3\).

Given that \(f(x)=3 x+1, g(x)=x^{2}-2 x-6,\) and \(h(x)=x^{3},\) find each of the following. $$(h \circ h)(2)$$

Given that \(h(x)=x+4\) and \(g(x)=\sqrt{x-1},\) find each of the following, if it exists. $$(h-g)(-4)$$

First, graph the equation and determine visually whether it is symmetric with respect to the \(x\) -axis, the \(y\) -axis, and the origin. Then verify your assertion algebraically. $$5 y=2 x^{2}-3$$

First, graph the equation and determine visually whether it is symmetric with respect to the \(x\) -axis, the \(y\) -axis, and the origin. Then verify your assertion algebraically. $$x^{2}+4=3 y$$

Given that \(f(x)=3 x+1, g(x)=x^{2}-2 x-6,\) and \(h(x)=x^{3},\) find each of the following. $$(h \circ h)(-1)$$