At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Just giving me an example of a) Is fine too im just trying to figure out how to set it up and solve it ^^
f(g(x)) means to simply put the expression, g(x), into f(x) in place of all instances of the variable x. Think of it like a search-and-replace, where every x in the "outer function" (in this case, f(x)) is replaced by the inner function, in this case (5x + 6). So you get f(g(x)) = 10 - (5x + 6) = 4 - 5x Now can you try the other 2?
f(g(x)) just applies you put the function g(x) where ever there is an x in f(x). So, \[f(g(x)) = 10-(5x+6)\] do so similarly with others.
@DebbieG Ok so you got 4 - 5x by 10 - 6 and 5x being by it self? so b) would be 5(10 - x) + 6 = 50x + 6 ?
Your distribution is wrong, but yet you get the point :)
\[g(f(x)) = 5(10-x)+6 \implies 50-5x+6\]
Yes, 5(10 - x) + 6, but 5(10 - x) + 6 != 50x + 6 I don't really understand what you mean by, "Ok so you got 4 - 5x by 10 - 6 and 5x being by it self?"
@DebbieG I was trying to see if i understood how you did it with my way of explaining how i took what you did. If that clears it up
@Astrophysics Ok so would that mean f(f(x)) 10 - (10 - x) = 10 - 10x?
\[f(f(x)) = 10 - (10-x)\]
@Astrophysics Thank you so much ^^ That was easier then i thought lol
Note that there is a "negative 1" there
there is another notation for these problems a) f(g(x)) <--- the same as f o g b) g(f(x)) <--- the same as g o f c) f(f(x)) <--- the same as f o f Looks like more textbooks are starting to get rid of the letter circle letter notation
Ah yes, when I was learning this, we had to do it both ways
I think it may have confused people, because it was written as such f o g (x)
I had to read right to left when I had that in my textbook
mine was strictly the letter o letter notation
xD Yeah, it was tricky at first