Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Writing functions as a composition of two simpler functions?
I don't understand this concept and my math textbook appears to not even teach the concept at all.
Write each of the following functions as a composition of two simpler functions:
(a) y = (x − 11)^5
(b) y = 3sqrt(1 + x^2)
(c) y = 2(x − 3)^5 − 5(x − 3)^2 + 0.5(x − 3) + 11
(d) y = 1/(x^2 + 3)
(e) y = sqrt(sqrt(x) + 1)
(f) y = 2 - sqrt(5 - (3x - 1)^2)
3 Answers
- EvanLv 61 decade agoFavorite Answer
Composition of two functions is like f(x), g(x) and g(f(x)). One function inside another.
basically doing two operations
In the first one, you are subtracting 11, and taking that expression to the 5th power. Those can be considered two functions
f(x) = x - 11
g(x) = x^5
g(f(x)) = g(x - 11) = (x-11)^5
In the second example, you are squaring x and adding 1, then you are taking 3 times the square root of that whole thing, so one breakdown is
f(x) = x^2 + 1
g(x) = 3*sqrt(x) [Just make the inside part "x" and make what's really inside the other function]
Similarly for d you can do something like
f(x) = x^2 + 3
g(x) = 1/x
The hard one is (c)
The whole thing is a polynomial in terms of (x-3) so try
f(x) = x-3
g(x) = 2x^5 - 5x^2 + 0.5x + 11
I will leave the others to you.
- Anonymous5 years ago
in case you elect to discover approximately technological information study some technological information books. The Bible, Bhagavad Gita and Koran will inform you in simple terms some info approximately technological information. The Koran and ahadith even have inaccuracies alongside with Mohammed claiming the earth is like an egg, which it extremely is not - it extremely is broader around the Equator, no longer slimmer. Given mohammed claimed a majority of those issues have been revelations of Allah, does that no longer surely make him a liar? ought to this kind of person be depended on in as 'final prophet of Allah'? Does the real God lie?
