Mr. Tarrou introduces inverse functions, explaining how to determine if two functions are inverses through composition. He demonstrates finding inverses both graphically and algebraically, emphasizing the importance of switching x and y variables and reflecting graphs over the line y=x. The video includes examples and verification of inverse functions using the composition process, ensuring the functions meet the criteria of one-to-one functions.

What is the first step in checking if two functions are inverses?

• Solve for y

• Switch the x and y variables

• Perform the composition f(g(x)) and g(f(x))

• Reflect the graph over the line y=x

Tags

CCSS.HSF-BF.B.4B

What indicates that two functions are inverses of each other?

• f(g(x)) and g(f(x)) are undefined

• f(g(x)) and g(f(x)) are constants

• f(g(x)) = g(f(x)) = y

• f(g(x)) = g(f(x)) = x

Tags

CCSS.HSF-BF.B.4B

How do you graphically find the inverse of a function?

• By switching the x and y intercepts

• By reflecting the graph over the y-axis

• By reflecting the graph over the line y=x

• By rotating the graph 180 degrees

Tags

CCSS.HSF-BF.B.4C

What happens to the coordinates of a point when a graph is reflected over the line y=x?

• The y-coordinate becomes the x-coordinate

• The x-coordinate becomes the y-coordinate

• The coordinates are squared

• The coordinates are unchanged

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

• It must have a y-intercept

• It must pass both the vertical and horizontal line tests

• It must pass the vertical line test only

• It must be a linear function

What does it mean for a function to pass the horizontal line test?

• The function is linear

• Every y-value has a unique x-value

• The function has no inverse

• Every x-value has a unique y-value

How do you algebraically find the inverse of a function?

• By solving for x

• By switching the x and y variables and solving for y

• By taking the reciprocal of the function

• By reflecting the equation over y=x

Tags

CCSS.HSF-BF.B.4A

What is the result of performing the composition f(g(x)) for inverse functions?

• 0

• 1

• y

• x

Tags

CCSS.HSF-BF.B.4B

What does the notation f^-1(x) represent?

• The reciprocal of f(x)

• The inverse of f(x)

• The derivative of f(x)

• The square root of f(x)

Tags

CCSS.HSF-BF.B.4A

Why is it important to check both compositions f(g(x)) and g(f(x)) when verifying inverses?

• To ensure the function is linear

• To confirm the function passes the vertical line test

• To verify the inverse relationship in both directions

• To determine if the function is continuous

Tags

CCSS.HSF-BF.B.4B