We will conclude that:
- The domain of the exponential function is equal to the range of the logarithmic function.
- The domain of the logarithmic function is equal to the range of the exponential function.
<h3>
Comparing the domains and ranges.</h3>
Let's study the two functions.
The exponential function is given by:
f(x) = A*e^x
You can input any value of x in that function, so the domain is the set of all real numbers. And the value of x can't change the sign of the function, so, for example, if A is positive, the range will be:
y > 0.
For the logarithmic function we have:
g(x) = A*ln(x).
As you may know, only positive values can be used as arguments for the logarithmic function, while we know that:

So the range of the logarithmic function is the set of all real numbers.
<h3>So what we can conclude?</h3>
- The domain of the exponential function is equal to the range of the logarithmic function.
- The domain of the logarithmic function is equal to the range of the exponential function.
If you want to learn more about domains and ranges, you can read:
brainly.com/question/10197594
The question is incomplete. Here is the complete question.
As a part of city building refurbishment project, architects have constructed a scale model of several city builidings to present to the city commission for approval. The scale of the model is 1 inch = 9 feet.
The model includes a new park in the center of the city. If the dimensions of the park in the model are 9 inches by 17 inches, what are the actual dimensions of the park?
Answer: 81 feet by 153 feet
Step-by-step explanation: <u>Unit</u> <u>Scale</u> is a ratio comparing actual dimensions of an object to the dimensions of model representing the actual object.
In the refurbishment project, the unit scale is given by
1 inch = 9 feet
So, the dimensions of the new park in actual dimensions would be
1 inch = 9 feet
9 inches = x
x = 9.9
x = 81 feet
1 inch = 9 feet
17 inches = y
y = 17.9
y = 153 feet
The actual dimensions of the new park are 81 feet by 153 feet.
Answer:
60
Step-by-step explanation:
Cot is the same as 1/tan so:

By rearranging the equation, we get:

By taking the inverse tan, we get:
