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Math 170 Functions, Data, and Models. 10 Composition and Inverse Section 2.4. Basic Concepts. 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.

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Math 170 functions data and models

Math 170 Functions, Data, and Models

10 Composition and Inverse

Section 2.4


Basic concepts
Basic Concepts

  • 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


Pond example
Pond Example

  • 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.


Graph and table example
Graph and Table Example

  • Suppose is defined by the graph and is defined by the table.

  • Find , , and .

  • Find and .


Pendulum example
Pendulum Example

  • The period, , of a pendulum of length is given by , where is a constant.

  • Find a formula for and explain its meaning.


Gdp example
GDP Example

  • 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 ?


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