91Ó°ÊÓ

\(g(x)=\frac{1}{5} \sqrt{x-3}\)

Use a graphing calculator to evaluate \((f+g)(x),(f-g)(x),(f g)(x)\), and \(\left(\frac{f}{g}\right)(x)\) when \(x=5\). Round your answer to two decimal places. $$ f(x)=4 x^4 ; g(x)=24 x^{1 / 3} $$

Biologists have discovered that the shoulder height \(h\) (in centimeters) of a male Asian elephant can be modeled by \(h=62.5 \sqrt[3]{t}+75.8\), where \(t\) is the age (in years) of the elephant. Determine the age of an elephant with a shoulder height of 250 centimeters.

\(\sqrt{2} \cdot \sqrt{72}\)

Evaluate the expression without using a calculator. (See Example 2.) \(81^{3 / 4}\)

In an amusement park ride, a rider suspended by cables swings back and forth from a tower. The maximum speed \(v\) (in meters per second) of the rider can be approximated by \(v=\sqrt{2 g h}\), where \(h\) is the height (in meters) at the top of each swing and \(g\) is the acceleration due to gravity \(\left(g \approx 9.8 \mathrm{~m} / \mathrm{sec}^2\right)\). Determine the height at the top of the swing of a rider whose maximum speed is 15 meters per second.

In Exercises 13–20, find the inverse of the function. Then graph the function and its inverse. $$ f(x)=-3 x $$

\(f(x)=\frac{1}{2} \sqrt[3]{x+6}\)

Use a graphing calculator to evaluate \((f+g)(x),(f-g)(x),(f g)(x)\), and \(\left(\frac{f}{g}\right)(x)\) when \(x=5\). Round your answer to two decimal places. $$ f(x)=7 x^{5 / 3} ; g(x)=49 x^{2 / 3} $$

\(\sqrt[3]{16} \cdot \sqrt[3]{32}\)