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Brandyn Moore PhD

Feb 20, 2025

The one-to-one functions g and h are defined as follows, please help?

The one-to-one functions g and h are defined as follows.g = { (-9,-5), (-4,7), (-2,3), (7,4) }h(x) = 3x + 14Find the following.g^-1 (7) = h^-1 (x) =(h o h^-1) (5) =
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2 Answers

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Major Spinka DVM

Feb 20, 2025

For the first one, you're finding the inverse. So, the input of the inverse function is the range of the original function, and the output of the inverse function is the domain of the original function. Thus, g^-1(7) = -4. For the second one, just find the inverse. So, h^-1(x) = (x - 14) / 3.For the last one, you are composing the original function with its inverse. Notice that h o h^-1(x) = (3x + 14 - 14) / 3 = x. So, h o h^-1(5) = 5.... Show More
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M
Major Spinka DVM

Feb 20, 2025

g⁻¹(7) = -4h⁻¹(x) = (x - 14) / 3(h o h⁻¹)(x) = x for any x, so (h o h⁻¹)(5) = 5.... Show More
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