Writing the inverse of another function as an inverse function

The video tutorial explains how to find the inverse of a function, specifically F(x) = 2x^2 - 3. It covers the step-by-step method to rewrite the function as an equation, swap variables, and solve for Y using inverse operations. The tutorial emphasizes the importance of including both positive and negative square roots but highlights that only the positive value is used to maintain the function's integrity.

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

• Divide by 2

• Take the square root

• Add 3 to both sides

• Replace F(x) with y

After swapping x and y, what operation is performed next?

• Subtract 3

• Divide by 2

• Add 3

• Multiply by 2

Why is it necessary to include both positive and negative square roots initially?

• To make the function continuous

• To simplify the equation

• To ensure the equation is balanced

• To account for all possible solutions

Why do we only consider the positive square root when writing the inverse as a function?

• To match the original function

• To avoid complex numbers

• To simplify calculations

• To ensure the inverse is a function

What is the final form of the inverse function?

• F inverse of x = 2(x + 3)

• F inverse of x = (x + 3)^2 / 2

• F inverse of x = -sqrt(x + 3) / 2

• F inverse of x = sqrt(x + 3) / 2