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 + 14

Find the following.

g^-1 (7) =

h^-1 (x) =

(h o h^-1) (5) =

2 Answers

  • 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.

  • g⁻¹(7) = -4

    h⁻¹(x) = (x - 14) / 3

    (h o h⁻¹)(x) = x for any x, so (h o h⁻¹)(5) = 5.

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