College Algebra Test 2 Study Guide

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The graph of f Superscript negative 1 is a reflection of the graph of f about the line whose equation is​ _______.

y=x If the point​ (a,b) is on the graph of f​ , then the point​ (b,a) is on the graph of f Superscript negative 1 . The points​ (a,b) and​ (b,a) are symmetric with respect to the line yequals x. ​Thus, the graph of f Superscript negative 1 is a reflection of the graph of f about the line yequals x .

If the function g is the inverse of the function​ f, then f left parenthesis g left parenthesis x right parenthesis right parenthesis equals x and g left parenthesis f left parenthesis x right parenthesis right parenthesis equals x.

The function g is the inverse of the function​ f, so the changes made to x by the function g are undone by the changes made by the function​ f, and finally yield the x​ itself, f left parenthesis g left parenthesis x right parenthesis right parenthesis equalsx. This​ "undoing" takes place in the other direction g left parenthesis f left parenthesis x right parenthesis right parenthesis equals​x; that​ is, the changes made to x by the function f are undone by the changes made by the function g.


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