Functions and Their Inverses

The video tutorial explains how to determine if two functions are inverses of each other. It introduces the functions f(x) = x^2 - 2 and g(x) = sqrt(x + 2) and describes the tests needed to verify if they are inverses. The first test involves substituting g(x) into f(x) and checking if the result is x. The second test involves substituting f(x) into g(x) and again checking if the result is x. Both tests are performed, and it is concluded that the functions are indeed inverses of each other.

What is the function f(x) given in the video?

• x plus two

• x squared minus two

• x minus two

• x squared plus two

What is the function g(x) given in the video?

• x squared plus two

• The square root of x minus two

• The square root of x plus two

• x squared minus two

What must be true for two functions to be inverses of each other?

• They must have the same domain

• They must have the same range

• They must undo each other

• They must be linear

What is the result of substituting g(x) into f(x) in the first test?

• x

• x plus two

• x squared

• zero

What operation is performed on the square root in the first test?

• Subtraction

• Addition

• Squaring

• Multiplication

What is the result of substituting f(x) into g(x) in the second test?

• zero

• x plus two

• x

• x squared

What simplifies to zero in the second test?

• x squared

• x plus two

• Minus two plus two

• The square root of x

What is the final conclusion about the functions f(x) and g(x)?

• They are inverses

• They are the same function

• They are unrelated

• They are not inverses

What does f of g of x equal if the functions are inverses?

• x plus two

• zero

• x squared

• x

What does g of f of x equal if the functions are inverses?

• zero

• x plus two

• x squared

• x