Suppose a function can be described by 𝑦=𝑓(𝑥). The graphs of the function and the inverse function intersect when
Question
Suppose a function can be described by 𝑦=𝑓(𝑥). The graphs of the function and the inverse function intersect when
Solution
The graphs of a function and its inverse intersect when x = y. This is because, by definition, a function and its inverse swap inputs and outputs. So, any point (a, b) on the graph of the original function corresponds to a point (b, a) on the graph of the inverse function. Therefore, they intersect on the line y = x, where the input and output are the same.
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