Understanding Inverses of Exponential and Logarithmic Functions

What is the base of the exponential function discussed in the introduction?

• Base 5

• Base 10

• Base 3

• Base 2

Which line do the graphs of inverse functions reflect over?

• y = 2x

• y = x

• x = y

• x = 2y

What happens to the domain of an exponential function when it becomes a logarithmic function?

• It becomes the range

• It remains the same

• It doubles

• It becomes negative

What is the result of composing a function with its inverse?

• The original function

• Infinity

• The identity function

• Zero

How do you find the inverse of a function?

• Divide by 3

• Add 5 to x

• Multiply by 2

• Switch x and y, then solve for y

What is the inverse of multiplying by 2?

• Subtracting 2

• Multiplying by 3

• Adding 2

• Dividing by 2

In the example given, what is the inverse of the function y = 3 log base 5 of x?

• 5^(x/3)

• 3^(x/5)

• x^3

• log base 3 of x

What is the result when you apply the inverse operation to a logarithm?

• An exponent

• A subtraction

• A square root

• A division

How can you verify if two functions are inverses of each other?

• By composing them and checking if the result is x

• By checking if their graphs intersect

• By adding them together

• By subtracting one from the other

What is the inverse of the function y = 10^(x/6)?

• log base 10 of 6x

• x^6

• 10 log base 6 of x

• 6 log base 10 of x