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The one-to-one functions g and h are defined as follows.g=((-7, 5), (0, 7), (8, -2), (9, 0))

The one-to-one functions g and h are defined as follows.g=((-7, 5), (0, 7), (8, -2), (9, 0))-example-1
User Cphlewis
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The given functions are

g=((-7, 5), (0, 7), (8, -2), (9, 0))

and

h(x) = 2x - 13

To find g^-(0), we would find the value of x when y is 0

Looking at the function, where y = 0, x = 9

Thus,

g^-(0) = 9

The second function is

h(x) = 2x - 13

We would replace h(x) with y. We have

y = 2x - 13

The next step is to interchange x and y and solve for y. We have

x = 2y - 13

x + 13 = 2y

y = (x + 13)/2

We would replace y with h^-1(x). We have

h^-1(x) = (x + 13)/2

To find (h^-1 o h)(4), the first step is to find (h^-1 o h)(x). To do this, we would substitute x = 2x - 13 into h^-1(x) = (x + 13)/2. We have

(h^-1 o h)(x) = (2x - 13 + 13)/2

(h^-1 o h)(x) = 2x/2 = x

To find (h^-1 o h)(4), we would substitute x = 4 into (h^-1 o h)(x) = x. We have

(h^-1 o h)(4) = 4

User Peter Bernier
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