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Math 170 Functions, Data, and Models

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Math 170 Functions, Data, and Models

10 Composition and Inverse

Section 2.4

- An inverse function reverses the roles of inputs and outputs.

- The composition of two functions consists of using the output of one function as the input to the other function.

x

y = f(x)

f

g

z = g(y) = g(f(x))

x = f-1(y)

y

f-1

- A rock dropped into a pond creates a circular ripple whose radius increases at a steady rate of 10 cm per second.
- Find a formula for the radius of the ripple as a function of the time after the pebble was dropped into the pond.
- Find a formula for the area of the inside of the ripple as a function of its radius.
- Find a formula for the area of the inside of the ripple as a function of time after the pebble was dropped into the pond.
- Find a formula for the time after the pebble was dropped into the pond as a function of the radius of the ripple.

- Suppose is defined by the graph and is defined by the table.
- Find , , and .
- Find and .

- The period, , of a pendulum of length is given by , where is a constant.
- Find a formula for and explain its meaning.

- The gross domestic product (GDP) of the US is given by where is the number of years since 1990 and the units of are billions of dollars.
- What is meant by ?
- What is meant by ?