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:
7 < x
Step-by-step explanation:
−3 < x -10
Add 10 to each side
−3+10 < x -10+10
7 < x
So lets write this equation out. Let x be that number we are trying to find.
So five-sevenths is a fraction that is written like this
5/7
when you see the word "of" that means multiplication
so we can write the full equation.
(5/7)x = -35
now we can solve
Multiply both sides by 7
5x = -245
now divide by 5
and we get
x = -49
Answer:
A multiplicative inverse of a real number x is a real number y such that xy = 1. ... ((NOT GOOGLING DEF))
Step-by-step explanation:
"For every real number x, if x 0, then there is a real number y such that xy = 1.”
Answer:
<em>Axis of symmetry line is parallel to y- axis</em>
Equation of the parabola <em> ( x - ( -2 ))² = (y - 12 ) </em>
Step-by-step explanation:
<u><em>Explanation</em></u>:-
Given equation is y = x²+4 x+16
y = x²+2 (2 ) x + (2)² - (2)² + 16
y = ( x + 2 )² + 12
( x + 2 )² = y - 12
<em> ( x - ( -2 ))² = (y - 12 ) </em>
( x- h)² = 4 a ( y - k)
<em> Center (h ,k) = ( -2 , 12)</em>
<em> Here 4 a = 1 </em>
<em> a = 1/4</em>
<em>Focus S = ( h , K +a) = ( -2 , 12 + 0.25) = ( -2 , 12.25)</em>
<em>Axis of symmetry line is parallel to y- axis</em>
