College Algebra Test 2 Study Guide
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 equalsx; that is, the changes made to x by the function f are undone by the changes made by the function g.