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Section 4.1: Inverses

If the functions f and g satisfy two conditions:. Section 4.1: Inverses. g(f(x)) = x for every x in the domain of f . f(g(x)) = x for every x in the domain of g. then f and g are inverse functions . f is an inverse of g and g is an inverse of f. Determine whether f and g are inverses:.

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Section 4.1: Inverses

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  1. If the functions f and g satisfy two conditions: Section 4.1: Inverses g(f(x)) = x for every x in the domain of f f(g(x)) = x for every x in the domain of g then f and g are inverse functions. f is an inverse of g and g is an inverse of f

  2. Determine whether f and g are inverses: Section 4.1: Inverses f and g are inverses

  3. Method for determining the inverse of a function: Section 4.1: Inverses Solve for x:

  4. A function f has an inverse if and only if its graph is cut at most once by any horizontal line: Section 4.1: Inverses A function which passes the vertical and horizontal line tests has an inverse and is one-to-one.

  5. Graphically: Section 4.1: Inverses If f has an inverse, the graphs of the functions are reflections of one another about the line y = x.

  6. If the graph of f is always increasing or decreasing, then the function f has an inverse. Section 4.1: Inverses How can we show a function is always increasing or decreasing?

  7. The domain of the original is the range of the inverse. The range of the original is the domain of the inverse. Section 4.1: Inverses

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