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 value of (f/g)(-√3), we need to substitute -√3 into both f(x) and g(x) and then divide f(x) by g(x).
First, let's substitute -√3 into f(x):
f(-√3) = (-√3)^2 - 3
= 3 - 3
= 0
Now, let's substitute -√3 into g(x):
g(-√3) = 2(-√3) + 1
= -2√3 + 1
Since f(-√3) = 0 and g(-√3) = -2√3 + 1, we can find (f/g)(-√3) by dividing f(-√3) by g(-√3):
(f/g)(-√3) = f(-√3) / g(-√3)
= 0 / (-2√3 + 1)
= 0
Therefore, (f/g)(-√3) is equal to 0.
To find the value of (g/f)(-1/2), we need to substitute -1/2 into both g(x) and f(x) and then divide g(x) by f(x).
First, let's substitute -1/2 into g(x):
g(-1/2) = 2(-1/2) + 1
= -1 + 1
= 0
Now, let's substitute -1/2 into f(x):
f(-1/2) = (-1/2)^2 - 3
= 1/4 - 3
= -11/4
Since g(-1/2) = 0 and f(-1/2) = -11/4, we can find (g/f)(-1/2) by dividing g(-1/2) by f(-1/2):
(g/f)(-1/2) = g(-1/2) / f(-1/2)
= 0 / (-11/4)
= 0
Therefore, (g/f)(-1/2) is equal to 0.