X plus x equals what?
2 answers:
You might be interested in
Answer:
The radical notation is
Step-by-step explanation:
Given
Step 1 of 1
Write the expression using rational exponents.
Simplify
Learn more about radical notation, refer :
Answer:
The population alternates between increasing and decreasing
Step-by-step explanation:
<u><em>The options of the question are</em></u>
A) The population density decreases each year.
B) The population density increases each year.
C) The population density remains constant.
D) The population alternates between increasing and decreasing
we have
Find the value of
For n=2
Find the value of
For n=3
For n=4
For n=5
therefore
The population alternates between increasing and decreasing
Note that f(x) as given is <em>not</em> invertible. By definition of inverse function,
which is a cubic polynomial in with three distinct roots, so we could have three possible inverses, each valid over a subset of the domain of f(x).
Choose one of these inverses by restricting the domain of f(x) accordingly. Since a polynomial is monotonic between its extrema, we can determine where f(x) has its critical/turning points, then split the real line at these points.
f'(x) = 3x² - 1 = 0 ⇒ x = ±1/√3
So, we have three subsets over which f(x) can be considered invertible.
• (-∞, -1/√3)
• (-1/√3, 1/√3)
• (1/√3, ∞)
By the inverse function theorem,
where f(a) = b.
Solve f(x) = 2 for x :
x³ - x + 2 = 2
x³ - x = 0
x (x² - 1) = 0
x (x - 1) (x + 1) = 0
x = 0 or x = 1 or x = -1
Then can be one of
• 1/f'(-1) = 1/2, if we restrict to (-∞, -1/√3);
• 1/f'(0) = -1, if we restrict to (-1/√3, 1/√3); or
• 1/f'(1) = 1/2, if we restrict to (1/√3, ∞)