rachelmaddie
Full Member
- Joined
- Aug 30, 2019
- Messages
- 851
I’m confused with this problemCould the original question actually be asking for \(f(x) \cdot g(x) \)? I'm not sure what the "dot with a hole" means in the image!
Yes. It is a notation that I do not like for students first studying functions because it does not build on the parentheses convention that the student already knows.Actually, this link https://mathmaine.com/2010/02/22/function-notation/ says that the open circle implies function of a function
Therefore g( f(x) ) is the correct interpretation. Please continue as of post#2, since JeffM is correct that there's a problem with your work.
What corrections do I have to make?Actually, this link https://mathmaine.com/2010/02/22/function-notation/ says that the open circle implies function of a function
Therefore g( f(x) ) is the correct interpretation. Please continue as of post#2, since JeffM is correct that there's a problem with your work.
Take a look at post # 2.What corrections do I have to make?
The result is 4x^2 - 4x - 1Take a look at post # 2.
YES NOW CHECK IT. (It is best to check with two numbers other than 0 or 1, one positive and one negative, but you may not have time for that on a test.)The result is 4x^2 - 4x - 1
It looks fine to me.So, write it like this?
f(x) = 2x - 1
g(x) = x^2 - 2
(gof)(x) = g[f(x)] —>equation 1 (gof)(x) = g(2x - 1)
equation 2 = (2x - 1)^2 - 2
= 4x^2 + 1 - 4x - 2
= 4x^2 - 4x - 1
(gof)(x) = (2x - 1)^2 - 2 = 4x^2 - 4x + 1 - 2 = 4x^2 - 4x - 1