91Ó°ÊÓ

For the following exercises, find \(f^{-1}(x)\) for each function. \(f(x)=\frac{2 x+3}{5 x+4}\)

For the following exercises, determine whether the relation represents \(y\) as a function of \(x\). \(2 x+y^{2}=6\)

For the following exercises, find the average rate of change of each function on the interval specified for real numbers \(b\) or \(h\) in simplest form. \(b(x)=\frac{1}{x+3}\) on \([1,1+h]\)

For the following exercises, use each pair of functions to find \(f(g(x))\) and \(g(f(x))\). Simplify your answers. \(f(x)=x^{2}+1, \quad g(x)=\sqrt{x+2}\)

For the following exercises, find the domain of each function using interval notation. \(f(x)=\sqrt[3]{1-2 x}\)

For the following exercises, describe how the graph of the function is a transformation of the graph of the original function \(f\). \(y=f(x-4)\)

For the following exercises, find the domain of each function using interval notation. \(f(x)=\sqrt[3]{x-1}\)

For the following exercises, determine whether the relation represents \(y\) as a function of \(x\). \(y=-2 x^{2}+40 x\)

For the following exercises, use each pair of functions to find \(f(g(x))\) and \(g(f(x))\). Simplify your answers. \(f(x)=\sqrt{x}+2, \quad g(x)=x^{2}+3\)

For the following exercises, find the average rate of change of each function on the interval specified for real numbers \(b\) or \(h\) in simplest form. \(j(x)=3 x^{3}\) on \([1,1+h]\)