Given that f(x) = x^2 -3 and g(x) = 2x+1, find each of the follwing, if it exists.

Problem 1 (f/g)(-root3)

Problem 2 (g/f)(-1/2)

To find (f/g)(-√3) and (g/f)(-1/2), we need to substitute the given values into the respective functions and simplify the expressions.

Problem 1: (f/g)(-√3)

To find (f/g)(-√3), we need to substitute -√3 into the function f(x) and g(x) separately.

First, substitute -√3 into f(x):

f(x) = x^2 - 3

f(-√3) = (-√3)^2 - 3
= 3 - 3
= 0

Next, substitute -√3 into g(x):

g(x) = 2x + 1

g(-√3) = 2(-√3) + 1
= -2√3 + 1

Therefore, (f/g)(-√3) = 0 / (-2√3 + 1).

Problem 2: (g/f)(-1/2)

To find (g/f)(-1/2), we need to substitute -1/2 into the function g(x) and f(x) separately.

First, substitute -1/2 into g(x):

g(x) = 2x + 1

g(-1/2) = 2(-1/2) + 1
= -1 + 1
= 0

Next, substitute -1/2 into f(x):

f(x) = x^2 - 3

f(-1/2) = (-1/2)^2 - 3
= 1/4 - 3
= -11/4

Therefore, (g/f)(-1/2) = 0 / (-11/4).