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. Which statement best describes l⁻¹(x)?

1) The inverse function of l(t) is l⁻¹(x) = 0.8x
2) The inverse function of l(t) is l⁻¹(x) = 0.64x
3) The inverse function of l(t) is l⁻¹(x) = 0.625x
4) The inverse function of l(t) is l⁻¹(x) = 0.8x + 82

Answer 1

The inverse function of l(t) is given by the equation l⁻¹(x) = 0.8x - 65.6, which is obtained by rearranging the original function equation and solving for t.

Step-by-step explanation:

The inverse function of l(t) is found by solving the equation l(t)=1.25t + 82 for t. To find l⁻¹(x), or the amount of time it takes for there to be x liters in the tank, we need to rearrange the original equation to solve for t. First, we subtract 82 from both sides, giving us x - 82 = 1.25t.

Next, we divide both sides by 1.25, yielding t = (x - 82) / 1.25. Thus the inverse function is l⁻¹(x) = ((x - 82) / 1.25), which simplifies to l⁻¹(x) = 0.8x - 65.6. None of the options provided in the question are correct, as they do not account for subtracting the 82 before dividing by 1.25.