91Ó°ÊÓ

Find the inverse function of \(f\) $$ f(x)=1-x^{3} $$

Area of a Ripple \(A\) stone is dropped in a lake, creating a circular ripple that travels outward at a speed of 60 \(\mathrm{cm} / \mathrm{s}\) . (a) Find a function \(g\) that models the radius as a function of time. (b) Find a function \(f\) that models the area of the circle as a function of the radius. (c) Find \(f \circ g .\) What does this function represent?

A function \(f\) is given. (a) Sketch the graph of \(f .(b)\) Use the graph of \(f\) to sketch the graph of \(f^{-1} .(c)\) Find \(f^{-1} .\) $$ f(x)=3 x-6 $$

Determine whether the equation defines y as a function of x. (See Example 9.) \(x+y^{2}=9\)

Find the domain of the function. $$ f(x)=\frac{3}{\sqrt{x-4}} $$

Inflating a Balloon A spherical balloon is being inflated. The radius of the balloon is increasing at the rate of 1 \(\mathrm{cm} / \mathrm{s}\) . (a) Find a function \(f\) that models the radius as a function of time. (b) Find a function \(g\) that models the volume as a function of the radius. (c) Find \(g \circ f .\) What does this function represent?

Determine whether the equation defines y as a function of x. (See Example 9.) \(x^{2}+y=9\)

A function \(f\) is given. (a) Sketch the graph of \(f .(b)\) Use the graph of \(f\) to sketch the graph of \(f^{-1} .(c)\) Find \(f^{-1} .\) $$ f(x)=16-x^{2}, \quad x \geq 0 $$

Find the domain of the function. $$ f(x)=\frac{x^{2}}{\sqrt{6-x}} $$

Area of a Balloon A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 2 \(\mathrm{cm} / \mathrm{s}\) . Express the surface area of the balloon as a function of time \(t(\text { in seconds). }\)