Answer to Question #242035 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

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: $(𝑓/𝑔)(𝑥)=\frac{x^2+3}{2x-5}.$ Let us identify its domain. Since the denominator of $\frac{x^2+3}{2x-5}$ is equal to zero in the point $x=2.5,$ we conclude that the domain of the function $(𝑓/𝑔)(𝑥)$ is $(-\infty,2.5)\cup(2.5,+\infty).$