Master Determine if two functions are inverses of each other formally ex 2

The video tutorial explains how to determine if two functions are inverses by composing them in both orders and simplifying to see if the result is the identity function, X. It provides multiple examples, demonstrating the process of plugging one function into another, simplifying, and checking if the result is X. The tutorial also highlights common mistakes and clarifies the importance of verifying both compositions to confirm inverse relationships.

What is the identity function used to verify if two functions are inverses?

• 0

• 1/X

• X^2

• X

Why is it necessary to check both F of G of X and G of F of X?

• To ensure they are equal

• To find the domain

• To verify they simplify to X

• To calculate the range

In the first example, what operation is used to simplify a number divided by a fraction?

• Multiplication by reciprocal

• Subtraction

• Division by reciprocal

• Addition

What is the result when composing F of G of X in the first example?

• 0

• 1/X

• X

• 3X

What indicates that two functions are not inverses in the second example?

• The result is X

• The result is zero

• The result is 1

• The result is negative X

In the third example, what operations are identified as inverse operations?

• Addition and subtraction

• Multiplication and division

• Square and square root

• Logarithm and exponentiation

In the third example, what is the final result of G of F of X?

• X + 2

• X

• X^2

• X - 2