91Ó°ÊÓ

Use a graphing utility to graph each function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$f(x)=x^{3}+x+1$$

Use a graphing utility to graph \(f\) and \(g\) in the same viewing rectangle. In addition, graph the line \(y=x\) and visually determine if \(f\) and g are inverses. $$f(x)=4 x+4, \quad g(x)=0.25 x-1$$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If \(\left(\frac{f}{g}\right)(a)=0,\) then \(f(a)\) must be 0

Use a graphing utility to graph \(f\) and \(g\) in the same viewing rectangle. In addition, graph the line \(y=x\) and visually determine if \(f\) and g are inverses. $$f(x)=\frac{1}{x}+2, \quad g(x)=\frac{1}{x-2}$$

Use a graphing utility to graph \(f\) and \(g\) in the same viewing rectangle. In addition, graph the line \(y=x\) and visually determine if \(f\) and g are inverses. $$f(x)=\sqrt[3]{x}-2, \quad g(x)=(x+2)^{3}$$

Solve: \(3(6-x)=3-2(x-4)\).

If \(f(x)=6 x-4,\) find \(f(b+2) .\)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. Regardless of what quadratic function I graph, the graph is shaped like a bowl or an inverted bowl, so this indicates that the quadratic function has an inverse function.

Let \(f(x)=3 x-4\) and \(g(x)=x^{2}+6\) a. Find \(f(5)\) b. Find \(g(f(5))\)

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I'm working with the linear function \(f(x)=3 x+5\) and I do not need to find \(f^{-1}\) in order to determine the value of \(\left(f \circ f^{-1}\right)(17)\).