Finding the inverse of a function- Free Online Tutoring

The video tutorial covers the concept of functions and their inverses, explaining the conditions for a function to have an inverse. It uses graphical representations to illustrate how inverses work and provides a step-by-step guide to finding inverses of functions. The tutorial includes examples and practice problems to reinforce the learning process.

What is a necessary condition for a function to have an inverse?

• It must be a quadratic function.

• It must be a constant function.

• It must be a linear function.

• It must be a one-to-one function.

Which test can be used to determine if a graph represents a function?

• Parallel line test

• Horizontal line test

• Diagonal line test

• Vertical line test

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

• Graph the function

• Swap x and y

• Replace f(x) with y

• Solve for x

When finding the inverse of a function, what do you do after swapping x and y?

• Graph the function

• Solve for y

• Replace y with f(x)

• Check for one-to-one property

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

• f^(-1)(x) = x + 7

• f^(-1)(x) = 7 - x

• f^(-1)(x) = x - 7

• f^(-1)(x) = x / 7

Why does the function f(x) = x^2 not have an inverse?

• It is not a rational function.

• It is not a linear function.

• It is not a cubic function.

• It is not a one-to-one function.

What is the inverse of the function f(x) = (x - 1) / 5?

• f^(-1)(x) = 5x + 1

• f^(-1)(x) = x / 5 - 1

• f^(-1)(x) = (x + 1) / 5

• f^(-1)(x) = 5x - 1

What is the inverse of the function f(x) = x^3 + 2?

• f^(-1)(x) = (x - 2)^(1/3)

• f^(-1)(x) = (x - 2)^3

• f^(-1)(x) = (x + 2)^3

• f^(-1)(x) = (x + 2)^(1/3)

What happens when you take the square root while solving for the inverse of a function?

• You get two values for y.

• You get a negative value for y.

• You get no values for y.

• You get a single value for y.

What is the inverse of the function f(x) = 6x?

• f^(-1)(x) = 6x

• f^(-1)(x) = x + 6

• f^(-1)(x) = 6 / x

• f^(-1)(x) = x / 6