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: b) {-3, 0.5}
Step-by-step explanation:
The new equation is the original equation plus 6. Move the original graph UP 6 units. The solutions are where it crosses the x-axis.
+6 means it is a transformation UP 6 units.
Solutions are where it crosses the x-axis.
The curve now crosses the x-axis at x = -3 and x = 0.5.
Answer:
y=1, x=-1
Step-by-step explanation:
I used substitution **I'm not sure this is right but this is what I got!!!***
The value of x is -27
1/3(-27) + 7 = -2
-9 + 7 = -2
-2 = -2
Hope this helps!
Answer:
x = 5, y = 20
Step-by-step explanation:
Since AB and CD are parallel, then
∠ AOC and ∠ OCD are Alternate angles and congruent, thus
12x + 8 = 68 ( subtract 8 from both sides )
12x = 60 ( divide both sides by 12 )
x = 5
-------------------------------
∠ OCD and 5y + 12 are adjacent angles and supplementary, thus
5y + 12 + 68 = 180 , that is
5y + 80 = 180 ( subtract 80 from both sides )
5y = 100 ( divide both sides by 5 )
y = 20
