Isolating Logarithmic Functions and Inverses

The video tutorial explains how to find the inverse of a function. It begins by replacing f(x) with y, then switches x and y in the equation. The main task is solving for y, which involves isolating terms, adding constants, dividing, and exponentiating. The final step is to write the inverse function in correct notation. The tutorial concludes with the final answer, ensuring the viewer understands each step of the process.

What is the first step in finding the inverse of a function?

• Exponentiate both sides

• Replace f(x) with y

• Switch x and y

• Solve for y

What is the base of the logarithm used in the function?

• 3

• 4

• 7

• 9

What is the initial expression for y in terms of x?

• y = 3 * log base 4 of x - 9 + 7

• y = 4 * log base 3 of x - 7 + 9

• y = 3 * log base 4 of x + 9 - 7

• y = 4 * log base 3 of x + 7 - 9

In the process of finding an inverse, what do you do after replacing f(x) with y?

• Switch x and y

• Solve for x

• Multiply by a factor

• Add a constant

What is the equation after switching x and y?

• y = 4 * log base 3 of y + 7 - 9

• x = 4 * log base 3 of x + 7 - 9

• y = 4 * log base 3 of x + 7 - 9

• x = 4 * log base 3 of y + 7 - 9

What is the next step after switching x and y in the equation?

• Add 9 to both sides

• Divide both sides by 3

• Subtract 7 from both sides

• Multiply both sides by 4

How do you isolate the logarithmic term in the equation?

• Multiply by 3 and add 7

• Subtract 7 from both sides and multiply by 4

• Add 9 to both sides and divide by 4

• Divide by 3 and subtract 9

What operation is performed after adding 9 to both sides?

• Multiply by 3

• Divide by 4

• Add 7

• Subtract 7

What is the purpose of exponentiating both sides of the equation?

• To eliminate the logarithm

• To add a constant

• To solve for x

• To switch x and y

What is the result of exponentiating both sides of the equation?

• y = 3^(x/4) + 9

• y + 7 = 3^(x + 9/4)

• y = 3^(x + 9/4) - 7

• x = 3^(y + 9/4)