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
The equation of this sinusoidal function is either
f(x) = a sin(bx) + c
or
f(x) = a cos(bx) + c
Either way, the plot of f9x) has amplitude a, period 2π/b, and midline y = c.
If the period is π/2, then
2π/b = π/2 ⇒ b = 4
If the maximum value is 10 and the minimum value is -4, then
-4 ≤ a sin(4x) + c ≤ 10
-4 - c ≤ a sin(4x) ≤ 10 - c
-(4 + c)/a ≤ sin(4x) ≤ (10 - c)/a
Recall that sin(x) is bounded between -1 and 1. So we must have
-(4 + c)/a = -1 ⇒ a = c + 4
(10 - c)/a = 1 ⇒ a = -c + 10
Combining these equations and eliminating either variable gives
a + a = (c + 4) + (-c + 10) ⇒ 2a = 14 ⇒ a = 7
a - a = (c + 4) - (-c + 10) ⇒ 0 = 2c - 6 ⇒ c = 3
Finally, we have either
f(x) = a sin(bx) + c ⇒ f(0) = c = 3
or
f(x) = a cos(bx) + c ⇒ f(0) = a + c = 3
but the cosine case is impossible since a = 7.
So, the given function has equation
f(x) = 7 sin(4x) + 3
18 percent
= 18/100 = 0.18 Use your calculator.
So that is it as a decimal.
Answer:
B
Explanation: If u use a number line you will understand the concept. So it goes 2,1,0,-1,-2. That decreased 5 times.
Answer: The answer would be 8.2