I need to find the quotient function of the following:
Given that f(x)=x^2-3 and g(x)=2x+1 find each of the following if it exists:
a. (f/g)(-root3)
b. (g/f)(-1/2)
To find the quotient function, we need to divide the function f(x) by the function g(x).
a. To find (f/g)(-√3), we need to substitute -√3 into the quotient function.
First, let's calculate f(-√3) and g(-√3).
f(x) = x^2 - 3
So, f(-√3) = (-√3)^2 - 3 = 3 - 3 = 0.
g(x) = 2x + 1
So, g(-√3) = 2(-√3) + 1 = -2√3 + 1.
Now, we can calculate (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) = 0.
b. To find (g/f)(-1/2), we need to substitute -1/2 into the quotient function.
First, let's calculate f(-1/2) and g(-1/2).
f(x) = x^2 - 3
So, f(-1/2) = (-1/2)^2 - 3 = 1/4 - 3 = -11/4.
g(x) = 2x + 1
So, g(-1/2) = 2(-1/2) + 1 = -1 + 1 = 0.
Now, we can calculate (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) = 0.