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If the point [tex]\((5, -7)\)[/tex] is a known point on the graph of [tex]\(f(x)\)[/tex], then the point [tex]\(( \text{type your answer...} )\)[/tex] must be a point on the function [tex]\(f^{-1}(x)\)[/tex], the inverse of [tex]\(f\)[/tex].

Sagot :

GinnyAnswer
When dealing with functions and their inverses, it is important to understand that for any given point [tex]\((a, b)\)[/tex] on the function [tex]\(f(x)\)[/tex], the coordinates swap roles when considering the inverse function [tex]\(f^{-1}(x)\)[/tex]. That means for any point [tex]\((a, b)\)[/tex] on [tex]\(f(x)\)[/tex], the corresponding point on [tex]\(f^{-1}(x)\)[/tex] will be [tex]\((b, a)\)[/tex].

Given that the point [tex]\((5, -7)\)[/tex] lies on the graph of [tex]\(f(x)\)[/tex], we need to find the corresponding point on the inverse function [tex]\(f^{-1}(x)\)[/tex].

1. Identify the coordinates of the given point on [tex]\(f(x)\)[/tex]:
[tex]\[ (a, b) = (5, -7) \][/tex]

2. Swap the coordinates to find the corresponding point on [tex]\(f^{-1}(x)\)[/tex]:
[tex]\[ (b, a) = (-7, 5) \][/tex]

Thus, the point [tex]\((-7, 5)\)[/tex] must be a point on the graph of the inverse function [tex]\(f^{-1}(x)\)[/tex].
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