Inverse Functions and Their Properties

This video tutorial explains how to find the inverse of a given function, f(x) = √(3-x) + 4, by switching the x and y variables and solving for y. The process involves algebraic manipulation, including subtracting constants and squaring both sides of the equation. The tutorial also covers determining the domain of the inverse function, which is equivalent to the range of the original function, resulting in a domain of [4, ∞) for the inverse function.

What type of problem is being addressed in the video?

• Inverse functions quadratic square root

• Exponential growth

• Linear equations

• Logarithmic functions

What is the given function in the video?

• f(x) = 3x - 4

• f(x) = sqrt(3 - x) + 4

• f(x) = x^2 + 3

• f(x) = 2x + 5

What is the first step in finding the inverse function?

• Multiply by 2

• Switch x and y

• Add 4 to both sides

• Divide by 3

After switching x and y, what is the next step in solving for y?

• Divide by 4

• Subtract 4 from both sides

• Add 3 to both sides

• Multiply by 2

What operation is performed after subtracting 4 from both sides?

• Dividing by 2

• Adding 5

• Squaring both sides

• Taking the square root

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

• x - 4 squared

• x - 4

• y + 3

• 3 - y

What is the final form of the inverse function?

• x - 3 squared

• 3 - x - 4 squared

• 3 + x - 4 squared

• x + 4 squared

What is the final step in solving for the inverse function?

• Subtracting 5

• Adding 3 to both sides

• Dividing by negative 1

• Multiplying by 2

What is the domain of the inverse function?

• 0 to infinity

• Negative infinity to 4

• 4 to positive infinity

• 3 to 10

Why is the domain of the inverse function 4 to infinity?

• Because the original function is undefined

• Because the inverse function is linear

• Because the original function is quadratic

• Because the range of the original function is 4 to infinity