Exploring Inverses of Exponential and Logarithmic Functions

What is the first step in finding the inverse of an exponential function?

• Isolate the exponential term

• Switch the positions of x and y

• Rewrite the function in logarithmic form

• Solve for x

In the process of finding an inverse, what must you do after switching x and y?

• Solve for x immediately

• None of the above

• Check if the function is isolated

• Rewrite the function in its alternate form

What base does the natural logarithm use?

• 1

• 10

• 2

• e

How do you isolate a term in a logarithmic function before rewriting it?

• Add constants to both sides

• No isolation is needed

• Multiply or divide both sides as needed

• Subtract constants from both sides

What is the inverse function of y = ln(x + 3)?

• y = e^(x) - 3

• y = e^(x + 3)

• y = e^(x) + 3

• y = e^(x - 3)

When rewriting a logarithmic function as an exponential function, what is crucial to check?

• The function's coefficients

• The function's base

• The function's exponent

• Whether the logarithmic term is isolated

What additional step is necessary when the term with the exponent is not isolated?

• Switch x and y again

• Perform operations to isolate the term

• Rewrite the function immediately

• None, proceed to solve for y

In the example, how was the logarithm isolated before rewriting it as an exponential function?

• By adding 7 to both sides

• By subtracting 7 from both sides

• By multiplying both sides by 2

• By dividing both sides by 2

What does the natural log of (x - 2) all over 2 signify in the context of inverses?

• None of the above

• It is a simple logarithmic function without any transformations

• It is the inverse of an exponential function with a base of e

• It represents a complex logarithmic function

Why is it important to ensure the logarithmic term is isolated before rewriting it?

• To make the equation more complex

• Isolation is not necessary

• To correctly apply the properties of logarithms

• To simplify the equation