Question

Modeling with Inverses

I'm confused with this whole section in this unit activity on my online class
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Answer 1

Explanation:

I will do the first one as an example.

To find the inverse of y = f(x), simply switch x and y, then solve for y.

y = 3 + 2 ln x

x = 3 + 2 ln y

x − 3 = 2 ln y

(x − 3) / 2 = ln y

y = e^((x − 3) / 2)

So the inverse function is:

f⁻¹(x) = e^((x − 3) / 2)

The original function told us the amount of water as a function of time.

The inverse function tells us the time as a function of the amount of water.