Finding the Inverse of a Function: Key Concepts and Techniques

What does the notation f^-1(x) represent?

• The function raised to the power of -1

• The inverse of the function f(x)

• The reciprocal of the function f(x)

• The function divided by -1

What is the graphical representation of an inverse function primarily characterized by?

• Rotation around the origin

• Reflection over the line y = x

• Reflection over the y-axis

• Translation along the x-axis

What is the inverse of the function f(x) = x^3?

• 3x

• x^3/3

• The cube root of x

• 3 * the square root of x

What does the line y = x represent in the context of inverse functions?

• The maximum value of the function

• The minimum value of the function

• The axis of symmetry for the inverse

• A reference for reflection of the function

How do the coordinates of a function and its inverse relate to each other?

• They are identical

• They are inversely proportional

• They are swapped

• They are squared

In the process of finding an inverse function algebraically, what is the first step?

• Switch the positions of x and y

• Reflect the function over the line y = x

• Substitute y for f(x)

• Divide both sides by the coefficient of x

What is the inverse function of f(x) = 7x - 4?

• 7x + 4

• 7 / (x - 4)

• (x + 4) / 7

• (x - 4) / 7

Why do we switch x and y when finding the inverse of a function?

• To eliminate the constant term

• To reverse the mapping from x to y

• To reflect the function over the y-axis

• To simplify the equation

What is the primary purpose of finding an inverse function?

• To find the derivative of the original function

• To determine the original function's maximum value

• To calculate the area under the curve of the original function

• To reverse the mapping from x to y

After switching x and y in the equation of a function, what is the next step to find its inverse?

• Substitute the original function back into the equation

• Isolate y on one side of the equation

• Multiply both sides by the leading coefficient

• Graph the function to verify accuracy