91Ó°ÊÓ

Find (a) \((f+g)(x)\), (b) \((f-g)(x)\), (c) \((f g)(x)\), and (d) \((f / g)(x)\). What is the domain of \(f / g\) ? \(f(x)=x^{2}\), \(g(x)=4 x-5\)

Find the coordinates of the point. The point is located three units to the left of the \(y\)-axis and four units above the \(x\)-axis.

(a) write the linear function \(f\) such that it has the indicated function values and (b) sketch the graph of the function. $$ f\left(\frac{1}{2}\right)=-6, f(4)=-3 $$

In Exercises 1-8, find the inverse function of \(f\) informally. Verify that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\). $$ f(x)=\sqrt[3]{x} $$

Determine whether the equation is an identity or a conditional equation. $$ x^{2}-8 x+5=(x-4)^{2}-11 $$

Find the coordinates of the point. The point is located eight units below the \(x\)-axis and four units to the right of the \(y\)-axis.

Determine whether the equation is an identity or a conditional equation. $$ x^{2}+2(3 x-2)=x^{2}+6 x-4 $$

Find (a) \((f+g)(x)\), (b) \((f-g)(x)\), (c) \((f g)(x)\), and (d) \((f / g)(x)\). What is the domain of \(f / g\) ? \(f(x)=2 x-5\), \(g(x)=4\)

In Exercises 1-8, find the inverse function of \(f\) informally. Verify that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\). $$ f(x)=x^{5} $$

$$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Input value } & 0 & 3 & 9 & 12 & 15 \\ \hline \text { Output value } & 3 & 3 & 3 & 3 & 3 \\ \hline \end{array} $$