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# Inverse Functions

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Let f(x) = 3x + 4 and g(x) = 2x + 8. If h(x) = f(g(x)) , then what is the inverse of h(x)?

Jul 28, 2021

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Let us simplify h(x) first. Plugging in the value of g(x) directly into h(x), we get:

h(x) = f(2x + 8)

We then can plug in 2x + 8 into f(x), to get:

h(x) = 3(2x + 8) + 4

h(x) = 6x + 28

In order to find the inverse of a function, we have to switch the x and y values first. Hence, we get:

y = 6x + 28

x = 6y + 28

We then have to solve for y. Solving for y, we get:

x - 28 = 6y

(x-28)/6 = y

Therefore, the inverse function of h(x) is $$h^{-1}(x) = \frac{x-28}{6}$$

Jul 28, 2021