Question

Modeling with Inverses

Answer 1

Step-by-step 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.