What statement is sometimes, but not always, true? Why
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What statement is sometimes, but not always, true? Why

[From: ] [author: ] [Date: 11-05-31] [Hit: ]
D. The inverse of an exponential function is a function.-A. Never. The parabola always fails the horizontal line tes.B.......
A. The inverse of a quadratic function is a function.
B. The inverse of a cubic function is a function.
C. The inverse of a logarithmic function is a function.
D. The inverse of an exponential function is a function.

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A. Never. The parabola always fails the horizontal line tes.
B. Sometimes. The function f(x) = x^3 has an inverse, but others, such as g(x) = x^3 - x does not. For example, g(-1) = g(0) = g(1) = 0, so g(x) is not one-to-one.
C. Always. One of the more popular definitions of a logarithm is the inverse of an exponential.
D. Almost always. There are only a trivial case where this is not the case, specifically f(x) = 1^x.

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the statement that is sometimes true is "The inverse of a logarithmic function is a function"

Because.... If the logarithmic function is one-to-one, its inverse exits. The inverse of a logarithmic function is an exponential function.

It's hard to explain so go to http://www.sosmath.com/algebra/logs/log4/log45/log45.html

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