SOLUTION: Find(𝑓 + 𝑔)(𝑥), (𝑓 - 𝑔)(𝑥), (𝑓 ∙ 𝑔)(𝑥), 𝑎𝑛𝑑 (𝑓/𝑔) (𝑥). 1. 𝑓(𝑥) = 3𝑥^2 − 𝑥 + 5 𝑎𝑛𝑑 𝑔(𝑥) = 2𝑥 − 3.

Algebra ->  Functions -> SOLUTION: Find(𝑓 + 𝑔)(𝑥), (𝑓 - 𝑔)(𝑥), (𝑓 ∙ 𝑔)(𝑥), 𝑎𝑛𝑑 (𝑓/𝑔) (𝑥). 1. 𝑓(𝑥) = 3𝑥^2 − 𝑥 + 5 𝑎𝑛𝑑 𝑔(𝑥) = 2𝑥 − 3.      Log On


   

Question 1155000: Find(𝑓 + 𝑔)(𝑥), (𝑓 - 𝑔)(𝑥), (𝑓 ∙ 𝑔)(𝑥), 𝑎𝑛𝑑 (𝑓/𝑔) (𝑥).
1. 𝑓(𝑥) = 3𝑥^2 − 𝑥 + 5 𝑎𝑛𝑑 𝑔(𝑥) = 2𝑥 − 3.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Find(𝑓 + 𝑔)(𝑥), (𝑓 - 𝑔)(𝑥), (𝑓 ∙ 𝑔)(𝑥), 𝑎𝑛𝑑 (𝑓/𝑔) (𝑥).
1.
f%28x%29+=+3x%5E2-x%2B5
g%28x%29=+2x-3

%28f+%2Bg%29%28x%29=3x%5E2-x%2B5%2B2x-3=3x%5E2%2Bx%2B2
%28f+-g%29%28x%29=3x%5E2-x%2B5-%282x-3%29=3x%5E2-x%2B5-2x%2B3=3x%5E2-3x%2B8

%28f%2Fg%29%28x%29=%283x%5E2-x%2B5%29%2F%282x-3%29
=> use long division and you will get
.......(3x%2F2%2B7%2F4
(2x-3)|3x%5E2-x%2B5
.......6x%5E2%2F2-9x%2F2
.......3x%5E2-9x%2F2..........subtract
............7x%2F2+%2B5
............7x%2F2+-21%2F4
................ 41%2F4->reminder
%28f%2Fg%29%28x%29=%283x%2F2%2B7%2F4%29%282x-3%29%2B41%2F4