Understanding Composite Functions and Inverses

The video tutorial explains how to work with functions s and t using input-output tables. It guides viewers through calculating the composite function s(t(x)) for specific values and explores whether the functions s and t are inverses. The tutorial emphasizes understanding the process of inputting values into functions and analyzing the results to determine inverse relationships.

What is the main task described in the introduction of the video?

• To calculate the derivative of function t.

• To solve a system of equations involving s and t.

• To complete the table for the composite function s(t(x)).

• To find the inverse of function s.

What is the first step in evaluating the composite function s(t(x))?

• Input x into function t.

• Find the inverse of function t.

• Calculate the derivative of s(t(x)).

• Input x into function s.

When x is 12, what is the output of the composite function s(t(x))?

• 61

• 18

• 12

• 8

What is the result of s(t(18))?

• 100

• 18

• 70

• 2

What is the output of s(t(70))?

• 100

• 12

• 70

• 7

What does the result of s(t(x)) = x suggest about the functions s and t?

• They are identical functions.

• They are derivatives of each other.

• They are inverses of each other.

• They are unrelated functions.

What is the significance of the output s(t(100))?

• It suggests that s and t are unrelated.

• It shows that s and t are identical.

• It confirms that s and t are inverses.

• It indicates a calculation error.

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

• Their ranges must be identical.

• Their composite functions must equal x.

• Their derivatives must be equal.

• Their domains must be identical.

How is the domain of function s related to function t?

• It is unrelated to function t.

• It is the same as the domain of function t.

• It is the same as the range of function t.

• It is the inverse of the domain of function t.

What conclusion is drawn about the functions s and t?

• They are inverses of each other.

• They are unrelated functions.

• They are derivatives of each other.

• They are identical functions.