Finding Inverse Functions Algebraically

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

• Graph the function

• Solve for y

• Switch x and y in the equation

• Rewrite the function with y instead of f(x)

After switching x and y in the equation, what should you do next?

• Graph the inverse function

• Solve for x

• Solve for y

• Rewrite the equation in function notation

Why is it important to isolate y when finding the inverse of a function?

• To ensure the function is properly defined

• To switch the roles of x and y effectively

• Because the inverse function is always expressed in terms of y

• To simplify the equation for graphing

How is the inverse function notation read?

• The inverse of f as a function of x

• The inverse of f is x

• f divided by x

• f to the negative 1 power of x

What is the inverse function of y = 2x - 3?

• y = (x + 3) / 2

• y = 2x + 3

• y = (x - 3) * 2

• y = (x - 3) / 2

What is the significance of the line y = x in the context of inverse functions?

• It separates the positive and negative values of the function

• It indicates the maximum value of the function

• It is the axis of symmetry for the graph of a function and its inverse

• It represents the domain of all functions

To find the inverse of a square root function, what is the first algebraic step after switching x and y?

• Divide both sides by the square root

• Square both sides

• Add 4 to both sides

• Subtract 4 from both sides

What is the inverse of the function y = sqrt(x - 4)?

• y = sqrt(x + 4)

• y = (x + 4)^2

• y = x^2 + 4

• y = sqrt(x) + 4

When finding the inverse of a quadratic function, why do we add a plus or minus sign after square rooting both sides?

• To account for the positive and negative roots

• To make the function invertible

• Because it's a requirement for all quadratic equations

• To simplify the equation further

What is the inverse of the function y = x^2 - 4?

• y = x^2 + 4

• y = plus or minus sqrt(x + 4)

• y = sqrt(x) - 4

• y = sqrt(x + 4)