Question

a tank is being filled with a liquid. ( l(t) ), given below, is the amount of liquid in liters in the tank after ( t ) minutes. ( l(t) = 1.25t + 82 ) complete the following statements. let ( l^{-1} ) be the inverse function of ( l ). take ( x ) to be an output of the function ( l ). that is, ( x = l(t) ) and ( t = l^{-1}(x) ). (a) which statement best describes ( l^{-1}(x) )?

• the amount of liquid (in liters) after ( x ) minutes.
• the ratio of the amount of liquid (in liters) to the number of minutes, ( x ).
• the reciprocal of the amount of liquid (in liters) after ( x ) minutes.
• the amount of time (in minutes) it takes to have ( x ) liters of liquid.

Explanation:

Step1: Understand inverse function definition

Given $L(t)$ gives liters $x$ at time $t$, so $x = L(t) = 1.25t + 82$. The inverse $L^{-1}(x)$ solves for $t$ in terms of $x$, meaning $t = L^{-1}(x)$ represents time to reach $x$ liters.

Step2: Match to statement

Compare to options: the inverse function gives the time (in minutes) needed to have $x$ liters of liquid.

Answer:

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