(1) <em>f(x)</em> = <em>x</em>² - 4<em>x</em> + 2, <em>g(x)</em> = 3<em>x</em> - 7
<em>(f</em> o<em> g) (x)</em> = <em>f(g(x))</em> = <em>f</em> (3<em>x</em> - 7)
= (3<em>x</em> - 7)² - 4(3<em>x</em> - 7) + 2
= (9<em>x</em>² - 42<em>x</em> + 49) + (-12<em>x</em> + 28) + 2
= 9<em>x</em>² - 57<em>x</em> + 79
(2) <em>g(x)</em> = -6<em>x</em> + 5, <em>h(x)</em> = -9<em>x</em> - 11
<em>(g</em> o <em>h) (x)</em> = <em>g(h(x))</em> = <em>g</em> (-9<em>x</em> - 11)
= -6(-9<em>x</em> - 11) + 5
= 54<em>x</em> + 66 + 5
= 54<em>x</em> + 71
(3) <em>f(x)</em> = √(2<em>x</em> - 5), <em>g(x)</em> = 5<em>x</em>² - 3
<em>(g</em> o <em>f) (x)</em> = <em>g(f(x))</em> = <em>g</em>(√(2<em>x</em> - 5))
= 5 (√(2<em>x</em> - 5))² - 3
= 5 (2<em>x</em> - 5) - 3
= 10<em>x</em> - 25 - 3
= 10<em>x</em> - 28
Answer:
A. The description represents an arithmetic sequence because the successive y-values have a common difference of 600
Step-by-step explanation:
The equation that this situation is describing would be
This would mean that this equation would be an arithmetic series
Answer: 21.2 ft
Step by step:
16 / 4 = 4
5.3 * 4 = 21.2
First person reads 9 pages more than other person in one week
<em><u>Solution:</u></em>
Given that,
One person reads 278 pages in 7-weeks
Therefore, 7 weeks = 278 pages
To find number of pages read in 1 week, divide 278 by 7
So one person reads approximately 40 pages in 1 week
Another person reads 31 pages each week
How many more pages does the first person reads than the second person
So we need to find the difference between them
Difference = 40 - 31 = 9
Thus one person reads 9 pages more than other person in one week
Answer:
- f(x) = x^5
- g(x) = 2x -6 . . . . . and see below for other possible definitions
Step-by-step explanation:
You are given an expression for the composition H(x) = f(g(x)) and asked to decompose it into two functions. One way to do that is to look at what is being done to the variable in the function H(x):
- the variable is multiplied by 2
- 6 is subtracted from the product
- the difference is raised to the 5th power.
One of the ways to create the functions g(x) and f(x) is to start at the top of this list and work your way down. Any subset of these transformations can be made into g(x). Then the rest of them are made into f(x).
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For example, using
g(x) = 2x
Then the rest of the list is f(x):
f(x) = (x-6)^5
so when you put 2x as the argument for f(x), you get ...
H(x) = f(g(x)) = f(2x) = (2x -6)^5 . . . . . the function we want.
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We could also do the first two steps of our list as g(x):
g(x) = 2x -6
f(x) = x^5
so
H(x) = f(g(x)) = f(2x -6) = (2x -6)^5
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If we like, we can factor the expression for H(x):
H(x) = (2(x -3))^5 = 32(x -3)^5
Using the methods above, we could write ...
g(x) = x -3
f(x) = 32x^5
so
H(x) = f(g(x)) = f(x -3) = 32(x -3)^5
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The multiplication and the addition can be made into several parts. We could choose ...
g(x) = (1/4)x -1
f(x) = (8x +2)^5
so
H(x) = f(g(x)) = f(1/4x -1) = (8(1/4x -1) +2)^5 = (2x -6)^5
