SOLUTION: explain why y= -x+b is its own inverse
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Question 479561: explain why y= -x+b is its own inverse
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Algebraically speaking, if f(x) = -x + b, then , also, because , which would satisfy the definition of an inverse function for f(x).
Graphically speaking, the graph of in general is just the symmetric rotation of the graph of f(x) about the line y = x. Since the line y = -x + b is perpendicular to the line y = x, a single symmetric rotation about the line y = x would yield the same graph, meaning the inverse function must be equal to itself.
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