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
In Cartesian coordinates, the region (call it
) is the set

In the plane
, we have

which is a circle with radius
. Then we can better describe the solid by

so that the volume is

While doable, it's easier to compute the volume in cylindrical coordinates.

Then we can describe
in cylindrical coordinates by

so that the volume is

Then the price of hot dog buns would go up, I assume.
If you were the owner of the leading hot dog bun company, and hot dog prices went down, then more people would need to buy hot dog buns. So if you wanted to profit from that you'd raise your prices a little bit to make more money.