Math  /  Algebra

QuestionComplete the sentence below. If f1f^{-1} denotes the inverse of a function ff, then the graphs of ff and f1f^{-1} are symmetric with respect to the line \qquad .
If f1f^{-1} denotes the inverse of a function ff, then the graphs of ff and f1f^{-1} are symmetric with respect to the line \square y=x2y=x+1y=xy=x2+1\begin{array}{l} y=x^{2} \\ y=x+1 \\ y=x \\ y=x^{2}+1 \end{array}

Studdy Solution
The line of symmetry for the graphs of a function and its inverse is the line y=x y = x . This is because the roles of x x and y y are swapped for the inverse function.
The sentence can be completed as follows:
If f1 f^{-1} denotes the inverse of a function f f , then the graphs of f f and f1 f^{-1} are symmetric with respect to the line y=x y = x .

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