A biochemical experiment involves combining together two pro

A biochemical experiment involves combining together two protein extracts. Suppose a function (t) monitors the amount (nanograms) of extract A remaining at time t (nanoseconds). Assume you know these facts: 1. The function is invertible; i.e., it has an inverse function. 2. (0) = 6, (1) = 5, (2) = 3, (3) = 1, (4) = 0.5, (10) = 0.

(a) At what time do you know there will be 3 nanograms of extract A remaining?

(b) What is 1 (0.5) and what does it tell you?

(c) (True or False) There is exactly one time when the amount of extract A remaining is 4 nanograms.

(d) Calculate (1 (1)) =

(e) Calculate 1 ((6)) =

(f) What is the domain and range of ?

Solution

(a) Since (2) = 3

so at, t=2 nanosecond there will be 3 nanograms of extract remaining.

(b) 1 (0.5)=4

Means that at time t=4 nanosecond, 0.5 nanogram extract remain

(c)True, but not in nanosecond, it may be in picosecond

(d)(1 (1)) = (3) =1

(e)1 ((6))=1 (0)=10

(f) Domain of is 0 to 10 and its range is 0 to 6