That funky circle in the middle is the composition of the function. It asks you to take a function as an input and to yield an output that's another function. It's one of the five function operations, along with adding, subtracting, multiplying, and dividing.
When you compose, you might find the notation w(u(x)) easier to understand. It's saying evaluate u then evaluate w.
For our functions, the compositions are:
u(w(x)) = u(2x²) = -(2x²) - 2 = -2x² - 2
w(u(x)) = w(-x - 2) = 2(-x - 2)² = 2(x² + 4x + 4) = =2x²+ 8x +8
Now we evaluate each composition at 4.
u(w(4)) = -2(4²) - 2 = -2(16) - 2 = -32 -2 = -34
w(u(4)) = -2(2²) +8(2) + 8 = -2(4) + 16 + 8 = -8 + 16 + 8 = 16.
Thus, u(w(4)) = -34 and w(u(4)) = 16.
Answer:
It very well could be
Step-by-step explanation:
It could be any type of wood, it doesn't matter weight, volume, or size
5/6 because there are 5 possible possibilities and 6 numbers on the dice I'm assuming that the dice has 6 faces.
Answer:
BC = 8 and EF = 8.
Step-by-step explanation:
Since triangle ABC and DEF are congruent to each other, BC corresponds with EF (as determined by the triangle names).
Set BC and EF equal to each other.
x + 6 = 3x + 2
Subtract x from both sides.
6 = 2x + 2
Subtract 2 from both sides.
4 = 2x.
Divide 2 on both sides.
x = 2.
Substitute 2 for x.
BC = 2 + 6
BC = 8
Since we already know that EF is congruent to BC, EF is also 8.
EC = 3(2) + 2
EC = 6 + 2
EC = 8
