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Maybe; the range of the original function is given, correct? If so, then calculate the range of the inverse function by using the original functions range in the original function. Those calculated extreme values are the range of the inverse function.

Suppose:

f(x) = x^3, with range of -3 to +3.

f(-3) = -27

f(3) = 27.

Let the inverse function of f(x) = g(y); therefore g(y) = y^(1/3).

The range of f(y) is -27 to 27.

If true, then

f(x) = f(g(y)) = f(y^(1/3)) = (y^(1/3))^3 = y

g(y) = g(f(x)) = g(x^3) = (x^3)^3 = x

Try by substituting the ranges into the equations, if the proofs hold, then the answer is true for the function and the range that you are testing. Sometimes, however, it can be false. Look at a transcendental function.

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โˆ™ 2010-04-07 22:31:20
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Q: If an inverse function undoes the work of the original function the original functions range becomes the inverse functions?
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