Question

f^(-1)(0) = 21 hours (c) interpret the meaning of f(3). the height of the pool lowers by f(3) feet every 3 hours it is pumped. the pool loses water by f(3) kiloliters every 3 hours it is pumped. the pool contains f(3) kiloliters of water after carl has pumped for 3 hours. the pool has 3 kiloliters of water after carl has pumped for f(3) hours. (d) interpret the meaning of f^(-1)(0). the pool initially contains f^(-1)(0) kiloliters of water. the pool will be completely drained in f^(-1)(0) hours. the pool level will be f^(-1)(0) feet high after all of the water is pumped out. when carl has completed his work there will be f^(-1)(0) kiloliters of water left in the pool. (e) use part (b) to complete the blanks. f(number) = 0 f^(-1)(number) = 3

Explanation:

(c) The function $f(t)$ represents the amount of water in the pool at time $t$ (in hours) while it is being pumped. So $f(3)$ is the amount of water (in kiloliters) in the pool after 3 hours of pumping.
(d) The inverse - function $f^{-1}(x)$ gives the time $t$ when the amount of water in the pool is $x$. So $f^{-1}(0)$ is the time when the amount of water in the pool is 0, i.e., the pool will be completely drained in $f^{-1}(0)$ hours.
(e) If $f(a)=0$, then $a$ is the time when the pool is empty. And if $f^{-1}(b) = 3$, then $b$ is the amount of water in the pool after 3 hours of pumping.

Answer:

(c) The pool contains $f(3)$ kiloliters of water after Carl has pumped for 3 hours.
(d) The pool will be completely drained in $f^{-1}(0)$ hours.
(e) $f(f^{-1}(0)) = 0$; $f^{-1}(f(3)) = 3$