The width of the rectangular pen is equal to 14 feet.
Answer:
The graph of this piece-wise function is attached below.
Step-by-step explanation:
Given the function
- A piece-wise function is a function which has multiple pieces.
- Each of the pieces have their own restrictions.
- The domain of a function is the set of input, or x, values for which the function is defined.
- The range is the set of all values taken by the function
As the piece
has the domain [-5, 3) and graph of this piece is attached below.
and
has the domain [3, 7) and graph of this piece is attached below.
So, the domain of the piece-wise function can be composed as [-5, 3) U [3, 7) and range has the interval
.
i.e.
Domain: [-5, 3) U [3, 7)
Range: ![\:\left[-1,\:27\right]](https://tex.z-dn.net/?f=%5C%3A%5Cleft%5B-1%2C%5C%3A27%5Cright%5D)
The graph of this piece-wise function is attached below.
<em>Keywords: piece-wise function, domain, range</em>
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Answer:
f^-1(x) = (x -2)/3
Step-by-step explanation:
To find the inverse function, swap x and y, then solve for y.
y = 3x +2 . . . . given function
x = 3y +2 . . . . inverse relation
x -2 = 3y . . . . subtract 2
(x -2)/3 = y . . . divide by 3
f^-1(x) = (x -2)/3 . . . . in functional form
9514 1404 393
Answer:
(a) 26 units
Step-by-step explanation:
The left-side vertical line extends from y = -3 to y = +3, so is 3-(-3) = 6 units long.
The bottom side horizontal line extends from x = -5 to x = 2, so is 2 -(-5) - 7 units long.
The sum of these two sides is 6 + 7 = 13 units. These two sides make up half of the perimeter, which is the total length of all four sides.
The perimeter is 2 × 13 units = 26 units.