Answer:
- The domain of f is x > 0.
- The range of f is all real numbers.
and
- The domain of f is the same as the range of the inverse function.
- The range of f is the same as the domain of the inverse function.
Step-by-step explanation:
All log functions without any additional terms added to it outside the operation have domain x>0 and all real number range.
When the inverse is found, (x,y) are switched to (y,x). This measn the range becomes the domain the domain becomes the range.
No they do not sorry that I wasn't very quick<span />
Answer:
Step-by-step explanation:
The dog's route and final facing direction are shown in the attached diagram.
<h3>Turns</h3>
The sequence of facing directions for right turns is ...
{N, E, S, W, N}
The sequence of facing directions for left turns is the reverse:
{N, W, S, E, N}
In total, the dog made 3 right turns and 2 left turns. The net change in facing direction is 3-2 = 1 right turn. The dog's initial facing direction is north, so its final facing direction is east, one right turn from north.
<h3>Distance</h3>
The distances traveled are ...
N 4, E 1, S 5, E 2, N 5.
The net change in position is north (4-5+5) = 4 miles, and east (1 +2) = 3 miles. The distance between the final point and the initial point is the hypotenuse of a right triangle with legs 4 miles and 3 miles. The Pythagorean theorem tells us that distance is ...
c² = a² +b²
c = √(a² +b²) = √(4² +3²) = √25 = 5
The smallest distance between the dog's final and initial points is 5 miles.