Answer:
The functions are inverses; f(g(x)) = x ⇒ answer D
⇒ answer D
Step-by-step explanation:
* <em>Lets explain how to find the inverse of a function</em>
- Let f(x) = y
- Exchange x and y
- Solve to find the new y
- The new y = 
* <em>Lets use these steps to solve the problems</em>
∵ 
∵ f(x) = y
∴ 
- Exchange x and y
∴ 
- Square the two sides
∴ x² = y - 3
- Add 3 to both sides
∴ x² + 3 = y
- Change y by
∴ 
∵ g(x) = x² + 3
∴ 
∴ <u><em>The functions are inverses to each other</em></u>
* <em>Now lets find f(g(x))</em>
- To find f(g(x)) substitute x in f(x) by g(x)
∵
∵ g(x) = x² + 3
∴ 
∴ <u><em>f(g(x)) = x</em></u>
∴ The functions are inverses; f(g(x)) = x
* <em>Lets find the inverse of h(x)</em>
∵ h(x) = 3x² - 1 where x ≥ 0
- Let h(x) = y
∴ y = 3x² - 1
- Exchange x and y
∴ x = 3y² - 1
- Add 1 to both sides
∴ x + 1 = 3y²
- Divide both sides by 3
∴ 
- Take √ for both sides
∴ ± 
∵ x ≥ 0
∴ We will chose the positive value of the square root
∴
- replace y by 
∴
640/79=8...8
79 goes through 640 8 times
Answer:
the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.
Step-by-step explanation:
if there is no mistake in the problem description, I read the following function :
C(x) = y = 0.3x² - 1.2x + 2
I don't know if you learned this already, but to find the extreme values of a function you need to build the first derivative of the function y' and find its solutions for y'=0.
the first derivative of C(x) is
0.6x - 1.2 = y'
0.6x - 1.2 = 0
0.6x = 1.2
x = 2
C(2) = 0.3×2² - 1.2×2 + 2 = 0.3×4 - 2.4 + 2 = 1.2-2.4+2 = 0.8
so, the minimum production level is costing $800 (0.8×$1000) per hour for 2000 (2×1000) items produced per hour.
Answer:
4/25 or 0.16
Step-by-step explanation:
your welcomeee
Answer:
x = 5.5
Step-by-step explanation:
Based on the Mid-segment theorem of a triangle, we would have the following:
EF = 2(AB)
AB = 7
EF = 2x + 3
Plug in the values
2x + 3 = 2(7)
Solve for x
2x + 3 = 14
Subtract 3 from each side
2x + 3 - 3 = 14 - 3
2x = 11
2x/2 = 11/2
x = 5.5
