Question

PLEASE HELPCoffee is being brewed in a drip coffee maker and is filling a carafe. Its rate of flow is not steady, but it is always positive. The carafe is large enough to contain all the coffee that will flow into it. The table below shows V, the total amount of coffee in the carafe measured in cubic inches, as a function of time t, measured in minutes, since the coffee first started dripping into the carafe.Select 3 correct answers from the choices below. Question 1 options:1) The function is invertible because the volume is always increasing as the time is increasing.2) The function is invertible because the volume is decreasing as the time is increasing.3) The function is not invertible.4) V(7) = 70.95) V(7) = 150.36) V-1(70.9) = 70.97)V-1(70.9) = 3.28) V-1(70.9) = 4.5

Answer 1

(1) A function is said to be invertible only if each input has a unique output. That is, each output is paired with exactly one input. As we can see from the table, each input, which is time, has a unique output, which is volume. Also as the volume is increasing the time is increasing.

Hence the answer here is (1) The function is invertible because the volume is always increasing as the time is increasing.

(2) We want to find V(7)

This is the volume when the time is t is 7 minutes.

From the table,

`V(7)=150.3`

Hence the answer is V(7) = 150.3

(3) We want to find

`V^(-1)(70.9)`

From the table, this is the time, when the volume is 70.9 cubic inches.

Looking at the table,

`V^(-1)(70.9)=3.2`

Hence the answer is 3.2