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Ch 9 – Properties and Attributes of Functions

Ch 9 – Properties and Attributes of Functions. 9.5 – Functions and their Inverses. What is the inverse of a function?. The inverse of a function f(x) “undoes” f(x) Its graph is a reflection of f(x) across the line y = x Sometimes, the inverse ends up NOT being a function.

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Ch 9 – Properties and Attributes of Functions

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  1. Ch 9 – Properties and Attributes of Functions 9.5 – Functions and their Inverses

  2. What is the inverse of a function? • The inverse of a function f(x) “undoes” f(x) • Its graph is a reflection of f(x) across the line y = x • Sometimes, the inverse ends up NOT being a function. • If the inverse is a function, then it is denoted as f-1(x)

  3. Horizontal-Line TestIf any horizontal line passes through more than one point on the graph of a relation, the inverse relation is NOT a function. The inverse relation is a function The inverse relation is not a function

  4. Use the horizontal-line test to determine whether the inverse of each relation is a function.

  5. Finding Inverses of functions • To find the inverse of a function, switch the x and y, then solve for y. • Example: Find the inverse of f(x) = x2

  6. Find the inverse f-1(x) of Determine whether it is a function, and state its domain and range.

  7. In a one-to-one function, each y-value is paired with EXACTLY one x-value. You can use composition of functions to verify that two functions are inverses. If f(g(x)) = g(f(x)) = x then f(x) and g(x) are inverse functions. When both a relation and its inverse are functions, the relation is called a one-to-one function.

  8. Determine by composition whether each pair of functions are inverses.

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