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Inverse function facts for kids

Kids Encyclopedia Facts

An inverse function is a concept of mathematics. A function will calculate some output y, given some input x. This is usually written f(x) = y. The inverse function does the reverse. Let's say g is the inverse function of f, then g(y) = x . Or otherwise put, g(f(x)) = x. An inverse function to f is usually called f^{-1}. It is not to be confused with 1/f, which is a reciprocal function.

Examples

If f(x) = x^3 over real x, then f^{-1}(x) = \sqrt[3]{x}.

To find the inverse function, swap the roles of x and y and solve for y. For example, y=e^x would turn to x=e^y, and then \ln x =y. This shows that the inverse function of y=e^x is y=\ln x.

Not all functions have inverse functions: for example, function f(x) = |x| has none (because |-1| = 1 = |1|, and f^{-1}(x) cannot be both 1 and -1), but every binary relation has its own inverse relation.

In some cases, finding the inverse of a function can be very difficult to do.

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