# Let f:Rise defined from R to R . find the solution of f(x) =f^-1 (x)?

# f(x) = x #

That is we seek a function that is its own inverse. One obvious such function is the trivial solution:

However, a more thorough analysis of the problem is of significant complexity as explored by Ng Wee Leng and Ho Foo Him as published in the Journal of the Association of Teachers of Mathematics.

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Check below.

graph{((y-(1-x^2))sqrtx)=0 [-7.02, 7.03, -5.026, 1.994]}

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The solution to ( f(x) = f^{-1}(x) ) is the set of points where the function f intersects its inverse function f^-1. In other words, the solution consists of all x values such that ( f(x) = f^{-1}(x) ). This can be found by solving the equation for x.

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