functions and math

Question

Given that f(x)=x²-7 and g(x)=-2x+3, find (f/g)(3/2) if it exists.

Please help explain how to solve.

Thanks!

Answer 1

f(3/2) = (3/2)^2 - 7 = 9/4 - 7 = -19/4

g(3/2) = -2(3/2) + 3 = -3 + 3 = 0

meaning that (f/g)(3/2) is undefined (does not exist) because it's not possible to divide by 0

Answer 2

Hi James,

 

(f/g)(x) = f(x)/g(x)

f(x) = x² -7 

f(3/2) = (3/2)² -7 = 9/4 -7 = -19/4

g(x) = -2x + 3

g(3/2)= -2(3/2) + 3 = -3+3 = 0

(f/g)(3/2) = f(3/2)/g(3/2)

 

Since g(3/2) = 0, (f/g)(3/2) does not exist (division by 0)