Answer:
1. f(g(4)) - g(f(4)) = -6
2. f(f(x)) = 125x^4 - 250x^2 + 120
3. a + b = 0
4. g(4) = -9
Step-by-step explanation:
1.
First we need to find f(4) and g(4):
f(4) = 4 + 3 = 7
g(4) = 3*4 + 5 = 17
Then, we find g(f(4)) = g(7):
g(7) = 3*7 + 5 = 26
And we find f(g(4)) = f(17):
f(17) = 17 + 3 = 20
so f(g(4)) - g(f(4)) = 20 - 26 = -6
2.
To find f(f(x)), we use the value of f(x) for every x in f(x):
f(f(x)) = 5*(f(x))^2 - 5 = 5*(5x^2 - 5)^2 - 5 = 5*(25x^4 - 50x^2 + 25) - 5
f(f(x)) = 125x^4 - 250x^2 + 120
3.
To find f(g(x)), we use the value of g(x) for every x in f(x):
f(g(x)) = g(x) + 6 = ax + b + 6 = 3x + 3
ax + (b+6) = 3x + 3 -> a = 3 and b = -3
a + b = 3 - 3 = 0
4.
If we assume g(x) = ax + b, we have:
g(f(x)) = a*(2x - 3) + b = 2ax - 3a + b = 5 - 4x
2a = -4 -> a = -2
-3a + b = 5
6 + b = 5 -> b = -1
g(x) = -2x - 1
g(4) = -2*4 - 1 = -9
Answer:
hoped to convince the United States to stay out of World War II
Explanation:
just took the quiz :)
Answer:
Step-by-step explanation:
4) parallel because 118° is a supplement to 62° and the corresponding angles are both 118°
5) NOT parallel. The labeled angles sum to 120° and would sum to 180° for parallel lines.
6) NOT parallel. see pic.
If parallel, extending a line to intersect ℓ₁ makes an opposite internal angle which would also be 48°. The created triangle would have its third angle at 180 - 90 - 48 = 42° which is opposite a labeled 48° angle, which is false, so the lines cannot be parallel
7)
b = 78° as it corresponds with a labeled angle above it
a = 180 - 78 = 102° as angles along a line from a common vertex sum to 180
f = is an opposite angle to 180 - 78 - 44 = 58° as angles along a line from a common vertex sum to 180
e = 180 - 90 - 64 = 26° as angles along a line from a common vertex sum to 180
c = 58° as it corresponds with f
d = 180 - 58 = 122° as angles along a line from a common vertex sum to 180