<span>The given function is ⇒⇒⇒ y = x² + 4x + 4
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To find the inverse of the function, we need to make x as a function of y and at the final step make a switch between x and y (i.e. make x as y and y as x)
y = x² + 4x + 4 ⇒⇒⇒ factor the quadratic equation
y = (x+2)(x+2)
y = (x+2)² ⇒⇒⇒ take the square root to both sides
√y = x+2
x = √y - 2 ⇒⇒⇒ x becomes a function of y
final step:
∴ y = √x - 2 ⇒⇒⇒ the inverse of the given function
So, as a conclusion:
f(x) = y = x² + 4x + 4 ⇒⇒⇒ the given function
f⁻¹(x) = y = √x - 2 ⇒⇒⇒ the inverse of the given function
Answer:
Approximately 338,000 people live in that area.
Step-by-step explanation:
In order to solve this problem we first need to find the area of the region, since it's delimited by a 7 miles radius, then we can assume it's a circular region. The area of the circle can be calculated by the following formula:
area = pi*r² = 3.14*(7)² = 153.86 miles²
Since the region has a density of 2200 people per square mile and the density is given by the formula:
density = number of people / area
We can find the number of people living in the region by doing:
number of people = density*area
Applying the data from the problem:
number of people = 2200*(153.86) = 338,492 people
Do u mean from the book or something?