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Math 170 Functions, Data, and Models

Math 170 Functions, Data, and Models. 44 Inverses Section 10.2. Basic Concepts.

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Math 170 Functions, Data, and Models

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  1. Math 170 Functions, Data, and Models 44 Inverses Section 10.2

  2. Basic Concepts • A function is a rule that assigns to each possible input exactly one output. A function can be expressed with words, tables, graphs, or formulas. Special types of functions include linear, quadratic, exponential, logarithmic, and trigonometric. • Suppose is a function with the property that each value of determines exactly one value of . Then has an inverse function, , and if and only if . • If a function has an inverse, it is said to be invertible.

  3. Table Inverses • Suppose is a function with the property that each value of determines exactly one value of . Then has an inverse function, , and if and only if . • If exists, provide its definition. If not, explain why not. • If exists, provide its definition. If not, explain why not. . Thus, cannot be defined

  4. Graph Inverses • If exists, sketch its graph. If not, explain why not. • If exists, sketch its graph. If not, explain why not.

  5. Graph Inverses Answers • does not exist because and so does not exist. • exists.

  6. Formula Inverses • For each of the following functions either find its inverse or explain why an inverse does not exist.

  7. Formula Inverses Answers • For each of the following functions either find its inverse or explain why an inverse does not exist. • exists but no formula

  8. Restricting the Domain • Restrict the domain of in two ways to obtain two inverse functions.

  9. Restricting the Domain Answer • Restrict the domain of in two ways to obtain two inverse functions.

  10. Word Inverses • Let be the temperature, in °C, of a piece of pottery seconds after removal from a kiln where . If exists, describe it. If not, explain why not. • is the number of seconds after removal from a kiln of the piece of pottery when it has reached the temperature °C. • Let w be the weight, in kilograms, of the instructor years after he was born where . If exists, describe it. If not, explain why not. • The instructor’s weight has fluctuated up and down since reaching adulthood.

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