Multiplying and Dividing Functions
Read this topicExplanations 4
- (Video) Multiplying and Dividing Functions by PatrickJMT Here's a video by PatrickJMT showing you how to multiply and divide different functions. He starts off by going over the…
By Alex Federspiel, Jonathan Heller, Joshua Siktar, Anusha Rahman
- Here are some different notations that you might come across when multiplying and dividing functions: (fg)(x)=f(x)⋅g(x)(fg)(x)=f(x)g(x), where g(x)≠0\begin{align} (fg)(x) &= f(x…
By Caroline K, Joshua Siktar, Anusha Rahman
- Function Operations: Multiplying and Dividing You've already learned how to add and subtract functions, so now it's time to learn about the other function operations: multiplyin…
By Jonathan Heller, Joshua Siktar, Anusha Rahman
- Multiplying and Dividing Functions Now that we've covered adding and subtracting functions, we can dive into the next lesson on the last two functions of function operations. Wh…
By Anusha Rahman
Problems 32
- Let f(x)=3xf(x) = 3xf(x)=3x and g(x)=5xg(x) = 5xg(x)=5x. What is (fg)(x)(fg)(x)(fg)(x)?
- Let f(x)=5x+3f(x) = 5x + 3f(x)=5x+3 and g(x)=x−2g(x) = x - 2g(x)=x−2. What is f(x)×g(x)?f(x)\times g(x)?f(x)×g(x)?
- Let f,gf,gf,g be functions such that, for all xxx, f(x)≠0f(x) \not= 0f(x)=0 and (fg)(x)=(fg)(x)(fg)(x) = \left(\frac{f}{g}\right)(x)(fg)(x)=(gf)(x). Which of these are possib…
- Let f(x)=(x−1)(x+3)f(x) = (x-1)(x+3)f(x)=(x−1)(x+3) and g(x)=x−1g(x) = x-1g(x)=x−1. What is (fg)(1)\left(\frac{f}{g}\right)(1)(gf)(1)?
- Let f(x)=4x2−9f(x)=4x^2-9f(x)=4x2−9 and g(x)=2x+3g(x)=2x+3g(x)=2x+3. Find (f⋅g)(x)(f\cdot g)(x)(f⋅g)(x).
- Let f(x)=4x2−9f(x)=4x^2-9f(x)=4x2−9 and g(x)=2x+3g(x)=2x+3g(x)=2x+3. Find (g/f)(x)(g/f)(x)(g/f)(x).
- Let f(x)=6x2+13x−5f(x)=6x^2+13x-5f(x)=6x2+13x−5 and g(x)=1−3xg(x)=1-3xg(x)=1−3x. Find (f⋅g)(x)(f\cdot g)(x)(f⋅g)(x).
- Let f(x)=6x2+13x−5f(x)=6x^2+13x-5f(x)=6x2+13x−5 and g(x)=1−3xg(x)=1-3xg(x)=1−3x. Find f(x)g(x)\frac{f(x)}{g(x)}g(x)f(x).
- If f(x)=−3x2f(x) = -3x^{2}f(x)=−3x2 and g(x)=−2x2+4xg(x) = -2x^{2}+4xg(x)=−2x2+4x, solve for (f⋅g)(3)(f \cdot g)(3)(f⋅g)(3).
- If f(x)=9x+4f(x)= 9x+4f(x)=9x+4 and g(x)=2g(x)=2g(x)=2, solve for fg(1)\dfrac{f}{g}(1)gf(1).
- If f(x)=3x2f(x) = 3x^{2}f(x)=3x2 and g(x)=1xg(x) =\dfrac{1}{x}g(x)=x1, solve for (g⋅f)(x)(g \cdot f)(x)(g⋅f)(x).
- Let f(x)=x2+3x+2f(x) = x^2 + 3x + 2f(x)=x2+3x+2 and g(x)=x+1g(x) = x + 1g(x)=x+1. What is f(x)g(x)\frac{f(x)}{g(x)}g(x)f(x), when x≠−1x\neq-1x=−1?
- Let f(x)=2x2+7x+6f(x) = 2x^2 + 7x + 6f(x)=2x2+7x+6 and g(x)=x+2g(x) = x + 2g(x)=x+2. What is f(x)g(x)\frac{f(x)}{g(x)}g(x)f(x), for x≠−2x\neq-2x=−2?
- Let f(x)=5x2+3f(x) = 5x^2 + 3f(x)=5x2+3 and g(x)=x+2g(x) = x + 2g(x)=x+2. What is (f⋅g)(x)(f\cdot g)(x)(f⋅g)(x)?
- Let f(x)=x+4f(x) = x+4f(x)=x+4 and g(x)=x2−4x+16g(x) = x^2 - 4x + 16g(x)=x2−4x+16. What is (f⋅g)(x)(f\cdot g)(x)(f⋅g)(x)?
- Let f(x)=x−2f(x) = x-2f(x)=x−2 and g(x)=x2+2x+4g(x) = x^2+2x+4g(x)=x2+2x+4. What is (f⋅g)(x)(f\cdot g)(x)(f⋅g)(x)?
- Let f(x)=x+1f(x) = x+1f(x)=x+1 and g(x)=x2−4xg(x) = x^2 - 4xg(x)=x2−4x. What is (f⋅g)(x)(f\cdot g)(x)(f⋅g)(x)?
- Let f(x)=x3−1f(x) = x^3 - 1f(x)=x3−1 and g(x)=x2+x+1g(x) = x^2+x+1g(x)=x2+x+1. What is f(x)g(x)\frac{f(x)}{g(x)}g(x)f(x)?
- Let f(x)=x2−16f(x) = x^2 - 16f(x)=x2−16 and g(x)=x+4g(x) = x+4g(x)=x+4. For all x≠−4x\neq-4x=−4, what is f(x)g(x)\frac{f(x)}{g(x)}g(x)f(x)?
- Let f(x)=2x−3f(x) = 2x - 3f(x)=2x−3 and g(x)=4x2+6x+9g(x) = 4x^2 + 6x + 9g(x)=4x2+6x+9. What is (f⋅g)(x)(f\cdot g)(x)(f⋅g)(x)?
- If f(x)=x2+3x−4f(x)=x^{2} +3x -4f(x)=x2+3x−4 and g(x)=x−1g(x) = x-1g(x)=x−1 what is fg(3)−f(3)\frac{f}{g}(3) - f(3)gf(3)−f(3)?
- Acceleration is calculated by dividing the change in time by the change in velocity. If V(x)=x3+2x+xV(x)=x^{3}+2x+xV(x)=x3+2x+x is the function for the change in velocity and T(…
- Kelsey is painting a right rectangular pyramid that contains a smaller right rectangular pyramid inside of it. She wants to make sure she has enough paint to paint the whole pyr…
- If f(x)=9x+1f(x)= 9x+1f(x)=9x+1 and g(x)=7xg(x)= 7xg(x)=7x, solve for (f⋅g)(4)(f \cdot g)(4)(f⋅g)(4).
- If f(x)=6x3+7x+10f(x)= 6x^3+7x+10f(x)=6x3+7x+10 and g(x)=4g(x)= 4g(x)=4, solve for (fg)(x)\left( \dfrac{f}{g}\right)(x)(gf)(x).
- If f(x)=x3+9x−1f(x)= x^3+9x-1f(x)=x3+9x−1 and g(x)=x+13g(x)= x+13g(x)=x+13, solve for (f⋅g)(2)(f \cdot g)(2)(f⋅g)(2).
- If f(x)=9f(x)= 9f(x)=9 and g(x)=13x4+5x3+17g(x)= 13x^4+5x^3+17g(x)=13x4+5x3+17, solve for (f⋅g)(1)(f \cdot g)(1)(f⋅g)(1).
- If f(x)=3x+8f(x)= 3x+8f(x)=3x+8 and g(x)=10x−5g(x)= 10x-5g(x)=10x−5, solve for (fg)(8)\left(\dfrac{f}{g}\right)(8)(gf)(8).
- f(x)=x+1g(x)=x2−4x+4\begin{align} f(x)&= x+1\\ g(x)&=x^2-4x+4 \end{align}f(x)g(x)=x+1=x2−4x+4 What is (fg)(x)(fg)(x)(fg)(x)?
- f(x)=x+1g(x)=x2−4x+4\begin{align}f(x)&=x+1\\ g(x)&=x^2-4x+4 \end{align}f(x)g(x)=x+1=x2−4x+4 What is (fg)(2)(fg)(2)(fg)(2)?
- The time it takes Jessica to do her work and the amount of work she does during the day depends on how many hours she slept the previous night. Let W(h)=h2−h−6W(h)=h^{2}-h-6W(h)…
- You want to figure out the hourly pay rate for your new job. Your boss told you that in terms of some secret variable xxx, the function that represents your pay is p(x)=20x+8p(x…