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 the values of the composite functions (f/g)(-√3) and (g/f)(-1/2), we first need to evaluate each function separately and then substitute the results into the other function.

Let's start by evaluating f(-√3) using the given function f(x) = x^2 - 3:
f(-√3) = (-√3)^2 - 3
= 3 - 3
= 0

Now, we can substitute this value into the function g(x) = 2x + 1 to find (f/g)(-√3):
(f/g)(-√3) = g(f(-√3))
= g(0)
= 2(0) + 1
= 1

Therefore, (f/g)(-√3) = 1.

Next, let's evaluate g(-1/2) using the function g(x) = 2x + 1:
g(-1/2) = 2(-1/2) + 1
= -1 + 1
= 0

We substitute this value into the function f(x) = x^2 - 3 to find (g/f)(-1/2):
(g/f)(-1/2) = f(g(-1/2))
= f(0)
= (0)^2 - 3
= -3

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