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Inverse Power Functions. If y = f(x) = a x b, then we may solve for x in terms of y by taking roots: x = f –1(y) = (y/a) 1/b = (1/a) 1/b y 1/b = k y 1/b,. where k = (1/a).

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Raising the base to a power and getting the logarithm (to that base) are also inverse that the expression y = 10x means y is equal to 10 raised.

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Finding the Inverse of an Exponential Function. I will go over three examples f of x is equal to 2 raised to the power of the quantity 3x-. This should be an easy.

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This algebra lesson explains how to find the inverse of a function.

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These functions are the logarithms, and they turn out to be . These functions are called power functions (note that the inverse of a power.

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A power function, in general, is: [math]f(x) = a*x^n[/math] The inverse of a power is the root with the same power as the power function.

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Warning: This notation is misleading; the "minus one" power in the function notation means "the inverse function", not "the reciprocal of". Don't confuse the two.

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EXAMPLE 4 Find the inverse of a power function The domain of f is restricted to nonnegative values of x. So, the range of f –1 must also be restricted to.

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Real Power Functions and Their Inverses In the case of the identity function the inverse is also the identity x = u, and in the case of the cubing function, the.