A tank is being filled with a liquid. , given below, is the amount of liquid in liters in the tank after minutes.

Question

L(t)= 2.5t + 5.5

Let L^-1 be the inverse function of L.

That is, x=L(t) and L^-1 (x).

(a) Which is the best statement that describes L^-1 (x)?

a: The ratio of the amount of liquid (in liters) to the number of minutes, x

b: The amount of time (in minutes) it takes to have x liters of liquid.

c: The reciprocal of the amount of liquid (in liters) after x minutes.

d: The amount of liquid (in liters) after x minutes

(b) L^-1 (x) =

(c) L^-1 (95) =

Answer 1

To find the inverse, replace the t and L(t) variables:

1. t = 2.5L(t) + 5.5
2. Now, solve for L(t) in the above function, using algebraic operations
3. The new L(t) function is the inverse of L(t) written as L^-1(t)
4. For L^-1(x), replace the t with an x in L^-1(t)
5. plug in, x = 95 to L^-1(x) to find L^-1(95)