Question

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:

For an inverse function \(L^{-1}(x)\), if the original function \(L(t) = x\) gives the amount of liquid \(x\) (in liters) after time \(t\) (in minutes), the inverse swaps the input and output. So \(L^{-1}(x) = t\) represents the time \(t\) (in minutes) needed to have \(x\) liters of liquid.

Answer:

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