Question

Hill's function is used to describe cooperative binding of proteins to

ligands (chemicals that have a biological function). If the concentration
x of ligand is written in the right units, then Hill's function can be written
in the following form:
f(x) =
k
X=
X
kix20
1+x
where you should assume that k is a positive constant greater than 1.
Complete parts (a) through (f) below.
(a) What are the roots of f(x)?
(Simplify your answer. Use a comma to separate answers as needed.)

Answer 1

The roots of Hill's function are ±√(-1/(ki)), resulting in imaginary roots.

Step-by-step explanation:

The roots of the function f(x) are the values of x that make f(x) equal to zero. In this case, to find the roots of f(x), we set f(x) = 0 and solve for x.

Using the given function, f(x) = k * X / (k * (ix^2) + 1), we can set f(x) = 0 and solve for x:

0 = k * X / (k * (ix^2) + 1)

k * (ix^2) + 1 = 0

ix^2 = -1/k

x^2 = -1/(ki)

x = ±√(-1/(ki))

Therefore, the roots of f(x) are ±√(-1/(ki)). Since k and i are both positive, the values inside the square root will be negative, resulting in imaginary roots.