Logarithmic Functions and Inverses

This video tutorial explains how to find the inverse of logarithmic functions and determine their domain and range. It covers the process of switching variables to find the inverse and rewriting logarithmic expressions in exponential form. The tutorial includes examples with different bases and emphasizes the relationship between the domain and range of original and inverse functions. The video concludes with an invitation for questions and suggestions for additional topics.

What must be true about the argument of a logarithmic function for it to be defined?

• It must be less than zero.

• It must be greater than zero.

• It must be equal to zero.

• It can be any real number.

What is the range of a logarithmic function?

• From zero to one

• From negative infinity to zero

• From zero to positive infinity

• From negative infinity to positive infinity

When finding the inverse of a function, what is the first step?

• Add 5 to both sides.

• Solve for x.

• Rewrite the function in exponential form.

• Switch the x and y variables.

In the inverse function, what does the base 'e' represent?

• The range of the function

• The exponent

• The natural logarithm base

• The original function

What is the domain of the inverse of an exponential function?

• From negative five to infinity

• From negative infinity to positive infinity

• From zero to infinity

• From three to infinity

In the example with a different base, what is the base of the logarithm?

• Base 2

• Base e

• Base 5

• Base 10

What is the domain of the function in the example with a different base?

• From negative five to infinity

• From negative infinity to positive infinity

• From three to infinity

• From zero to infinity

What is the range of the inverse function in the example with a different base?

• From zero to infinity

• From negative infinity to positive infinity

• From negative five to infinity

• From three to infinity

What is the final step in finding the inverse of a logarithmic function?

• Switch the x and y variables.

• Add 3 to both sides.

• Rewrite the function in exponential form.

• Solve for y.

What is the relationship between the domain of the original function and the range of its inverse?

• The range of the original is the domain of the inverse.

• The domain of the original is the range of the inverse.

• They are opposites.

• They are the same.