Adding and Subtracting Functions
Read this topicExplanations 5
- (Video) Adding and Subtracting Functions by PatrickJMT Here's a video by PatrickJMT showing you how to add and subtract functions. Once you've watched the video, try this relate…
By Alex Federspiel, Joshua Siktar, Anusha Rahman
- (Videos) Function Operations and Composition by mathman1024 Here's a video by mathman1024 explaining how to deal with adding, subtracting, multiplying, and dividing functions. T…
By Alex Federspiel, Joshua Siktar, Anusha Rahman
- (Videos) Operations with Functions by mathman1024 Here's a video by mathman1024 explaining function operations. (f+g)(x)=f(x)+g(x)(f−g)(x)=f(x)−g(x)(fg)(x)=f(x)⋅g(x)(fg)(x)=f(x)…
By Alex Federspiel, Anusha Rahman
- Operations with Functions We can add or subtract two functions and simplify. Addition Given two formulas f(x)f(x)f(x) and g(x)g(x)g(x), we can add two functions and simplify. (f…
By Eunji Kwon, Victor Wang
- Adding and Subtracting Functions Adding and subtracting functions can seem overwhelming at first, but there's a way to rewrite to make it easier to solve. To add or subtract fun…
By Anusha Rahman
Problems 21
- Given that f(x)=xf(x−1)f(x) = x f(x - 1)f(x)=xf(x−1), g(x)=(x+1)g(x−1)g(x) = (x + 1) g(x - 1)g(x)=(x+1)g(x−1), f(1)=7f(1) = 7f(1)=7, and g(1)=3g(1) = 3g(1)=3, calculate (f+g)(4)…
- Let f(x)=3x+5f(x) = 3x + 5f(x)=3x+5 and g(x)=7x+3g(x) = 7x + 3g(x)=7x+3. What is (f+g)(x)(f+g)(x)(f+g)(x)?
- Let f(x)=6x2+3x−5f(x) = 6x^2 + 3x - 5f(x)=6x2+3x−5 and g(x)=α(2x+3)(x−7)g(x) = \alpha(2x + 3)(x - 7)g(x)=α(2x+3)(x−7) for some real number α\alphaα. If (f−g)(f - g)(f−g) is line…
- Let f(x)=2xf(x) = 2^xf(x)=2x. Does there exist a function ggg such that (f−g)(f-g)(f−g) is linear?
- Fix f,g:R→Rf,g:\mathbb{R} \to \mathbb{R}f,g:R→R so that f(x)=x−4f(x) = x - 4f(x)=x−4 and g(y)=3y+12g(y) = 3y + 12g(y)=3y+12. What is (f+g)(z)(f+g)(z)(f+g)(z)?
- If f(x)=2xf(x)=2xf(x)=2x and g(x)=2x+1g(x)=2x+1g(x)=2x+1 then what is (f+g)(x)(f+g)(x)(f+g)(x)?
- If f(x)=x2+2f(x)=x^2+2f(x)=x2+2 and g(x)=3x+5g(x)=3x+5g(x)=3x+5 then what is (f+g)(x)(f+g)(x)(f+g)(x)?
- If f(x)=4x3+6x2−7x−10f(x)=4x^3+6x^2-7x-10f(x)=4x3+6x2−7x−10 and g(x)=2x4−3x3−x+9g(x)=2x^4-3x^3-x+9g(x)=2x4−3x3−x+9 then what is (f+g)(x)(f+g)(x)(f+g)(x)?
- If f(x)=3x+1f(x)=3x+1f(x)=3x+1 and g(x)=2x2−3x+1g(x)=2x^2-3x+1g(x)=2x2−3x+1 then what is (f−g)(x)(f-g)(x)(f−g)(x)?
- If f(x)=2x2−3x3+8f(x)=2x^2-3x^3+8f(x)=2x2−3x3+8 and g(x)=5x2+x−3g(x)=5x^2+x-3g(x)=5x2+x−3 then what is (g−f)(x)(g-f)(x)(g−f)(x)?
- If f(x)=10x−2f(x)=10x-2f(x)=10x−2 and g(x)=10x−8g(x)=10x-8g(x)=10x−8 what is f(x)−g(x)f(x)-g(x)f(x)−g(x)?
- If f(x)=5x2+2f(x) = 5x^{2} +2f(x)=5x2+2 and g(x)=14x−4g(x)= \dfrac{1}{4}x-4g(x)=41x−4, solve for (f+g)(2)(f+g)(2)(f+g)(2).
- If f(x)=4xf(x) = 4xf(x)=4x and g(x)=4−2xg(x) = 4-2xg(x)=4−2x, solve for (g−f)(−2)(g-f)(-2)(g−f)(−2).
- If f(x)=x2−x+3f(x) = x^{2}-x+3f(x)=x2−x+3 and g(x)=3−4x3g(x) = 3-4x^{3}g(x)=3−4x3, solve for (f+g)(x)(f+g)(x)(f+g)(x).
- If f(x)=x+4f(x)=x+4f(x)=x+4 and g(x)=3g(x)= 3g(x)=3, solve for (f−g)(7)(f-g)(7)(f−g)(7).
- Let f(x)=x+x2f(x) = x + x^2f(x)=x+x2 and g(x)=−x2+2x−1g(x) = -x^2 + 2x - 1g(x)=−x2+2x−1. What is the degree of (f+g)(x)(f+g)(x)(f+g)(x)?
- Let f(x)=x2+3f(x) = x^2 + 3f(x)=x2+3 and g(x)=2x+1g(x) = 2x + 1g(x)=2x+1. What is (f−g)(x)(f-g)(x)(f−g)(x)?
- Let f(x)=(x+1)2f(x) = (x+1)^2f(x)=(x+1)2 and g(x)=2x+1g(x) = 2x + 1g(x)=2x+1. What is (f−g)(x)(f-g)(x)(f−g)(x)?
- Let f(x)=4x2+1f(x) = 4x^2 + 1f(x)=4x2+1 and g(x)=x2+xg(x) = x^2 + xg(x)=x2+x. What is (f+g)(x)(f+g)(x)(f+g)(x)?
- Let f(x)=(x+2)2f(x) = (x+2)^2f(x)=(x+2)2 and g(x)=x2g(x) = x^2g(x)=x2. For what value of xxx does (f−g)(x)=0(f-g)(x) = 0(f−g)(x)=0?
- If f(x)=4x−7f(x) = 4x - 7f(x)=4x−7 and g(x)=2x−2,g(x) = 2x - 2,g(x)=2x−2, find f(x)−g(x).f(x) - g(x).f(x)−g(x). (Problem courtesy of Benjamin Qi)