Question

When two given functions, f(x) = x

2 + 3 and g(x) = 2x − 5, are divided with each other, a

new third function is obtained. Find (f/g)(x) and identify its domain.

Answer 1

$$(f/g)(x)=\dfrac{x^2+5}{2x-5}$$

$$2x-5\not=0=>x\not=\dfrac{5}{2}$$

$(f/g)(x)=\dfrac{x^2+5}{2x-5}$

$Domain: (-\infin, \dfrac{5}{2})\cup(\dfrac{5}{2}, \infin)$