Answer:
- f(x) = x^3
- g(x) = (2x+4)^2
Step-by-step explanation:
There are many ways to decompose h(x) into f(x) and g(x). The main purpose of the exercise seems to be to get you to think about the operations that are performed on x, then divide that list of operations into two parts.
In the function ...
h(x) = (2x +4)^6
the variable x is ...
- multiplied by 2
- 4 is added to the sum
- the sum is raised to the 6th power
Of course, the 6th power can be considered as the cube of a square or the square of a cube, if you like.
In the decomposition shown in the answer above, we have chosen to put most of this list in g(x), including the square of the sum. Then we have made f(x) be the cube of that square.
h(x) = f(g(x)) = (2x+4)^6
When f(x) = x^3, this is ...
h(x) = f(g(x)) = g(x)^3 = ((2x+4)^2)^3
so ...
g(x) = (2x+4)^2 . . . and . . . f(x) = x^3
_____
Other possible decompositions are ...
or
- g(x) = (x+2)
- f(x) = (2x)^6
or
or ... (many others)
Answer:
half a cup
Step-by-step explanation:
75% minus 25% is 50% aka 1 half
Answer:
2⁰ + 2¹+ 2⁵ +2³ = 43
Step-by-step explanation:
since 43 is odd, we know 2⁰ or 1 must be one of the sums
43 - 2⁰ = 42
42 - 2¹ = 40
16 = 2⁴
40-2(16) = 40 - 2⁵ = 8
8 = 2³
adding this all together
2⁰ + 2¹+ 2⁵ +2³ = 43
Answer:
r ≈ 22.44 ft
Step-by-step explanation:
The circumference (C) of a circle is calculated as
C = 2πr ( r is the radius ), then
141 = 2πr ( divide both sides by 2π )
= r , that is
r ≈ 22.44 ft ( to the nearest hundredth )
Answer:
...
Step-by-step explanation: