Answer to Question #242036 in Calculus for noor

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

$$(f/g)(x)=\dfrac{x^2+3}{2x-5}$$

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

$(f/g)(x)=\dfrac{x^2+3}{2x-5}$

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