Question

Unit activity: exponential and logarithmic functions

Answer 1

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.

Comparing the domains and ranges.

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:

$\lim_{x \to \infty} ln(x) = \infty \\\\ \lim_{x \to0} ln(x) = -\infty$

So the range of the logarithmic function is the set of all real numbers.

So what we can conclude?

• 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