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 
∴
Let 1993 = time 0 = 0.
Let 1999 = time 6 = 6
Let 2012 = time 19 = 19
So, a = 171 (million). First solve for k.
176 = 171 e^k6
176/171 = e^(k*6)
ln (176/171) = 6k
k = 1/6 ln (176/171)
So, in 2012 we have: P(19) = 171 e^(19k), where k = 1/6 ln (176/171)
Hope this helped!
Answer:
thanks for the points
Step-by-step explanation:
also
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For short term remembering: It really works if you take notes in class. I also found making connections to things you've experienced helps too.
For long term remembering - I found reviewing what you've learned recently is extremely useful. You can usually do this once in a couple of days until you're sure you can remember it.
Hope this helps!
Answer:
Real numbers for both
Step-by-step explanation:
The domain of a function is the set of values that the unknown t can adopt. For this function, t can be any real number as there are no restrictions for the t. Ir can be any positive number, 0, negative numbers, fractions, irrational numbers, whatever number you like.
The range of a function is the values that p(t) adopt when we replace the t value with any number. Here, again, it range is all real numbers. If you want p(t) to be positive it is possible, negative is possible, 0 is possible, and so on. If you like, you can verify it by replacing the numbers you like.
Something to know is that linear polynomial functions ALWAYS have their domains and ranges in real numbers.
