Master learn how to find the inverse of a function

The video tutorial explains how to find the inverse of a function through a step-by-step process. It covers replacing F of X with Y, swapping X and Y, and solving for Y using inverse operations. Several examples are provided, including linear, negative coefficient, cubic, quadratic, and reciprocal functions, demonstrating the application of these steps to find the inverse function.

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

• Swap x and y

• Replace f(x) with y

• Graph the function

• Solve for x

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

• To simplify the equation

• To eliminate fractions

• To reflect the function over the line y = x

• To make the function linear

What is the inverse of the function f(x) = 2x?

• f^(-1)(x) = x - 2

• f^(-1)(x) = x + 2

• f^(-1)(x) = 2x

• f^(-1)(x) = x / 2

How do you find the inverse of a cubic function like f(x) = x^3 - 2?

• Multiply both sides by 3

• Subtract 2 from both sides, then square the result

• Add 2 to both sides, then take the cube root

• Swap x and y, then solve for y

What is the inverse of the function f(x) = (x + 5)^2?

• f^(-1)(x) = sqrt(x) - 5

• f^(-1)(x) = x^2 - 5

• f^(-1)(x) = sqrt(x + 5)

• f^(-1)(x) = x - 5

How do you handle a function with a variable in the denominator when finding its inverse?

• Add the variable to both sides

• Multiply by the reciprocal

• Subtract the variable from both sides

• Square both sides

What is the inverse of the function f(x) = 1/x?

• f^(-1)(x) = 1/x

• f^(-1)(x) = x

• f^(-1)(x) = x^2

• f^(-1)(x) = -x