Radical Equations and Relationships Review (Test A)

Front

What is the definition of inverse functions?

Back

Inverse functions are functions that 'undo' each other. If f(x) is a function, then its inverse f⁻¹(x) satisfies the condition f(f⁻¹(x)) = x and f⁻¹(f(x)) = x.

Front

How do you determine if two functions are inverses of each other?

Back

To determine if two functions f(x) and g(x) are inverses, you need to check if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the formula for the volume of a cylinder?

Back

Front

What is the relationship between the radius and height of a cylinder if they are equal?

Back

Front

What is the formula for hang time in relation to jump height?

Back

Front

How do you find the height of a jump given the hang time?

Back

Front

What is the inverse of the function f(x) = -√(x+4)?

Back

The inverse function is f⁻¹(x) = x² - 4 with a domain restriction of x ≤ 0.

Front

What does it mean for a function to have a domain restriction?

Back

A domain restriction limits the set of input values (x) for which the function is defined, ensuring that the function remains valid.

Front

What is the significance of the composition of functions?

Back

The composition of functions allows us to combine two functions into a single function, which can help in determining relationships such as whether two functions are inverses.

Front

What is the graphical representation of inverse functions?

Back

The graphs of inverse functions are reflections of each other over the line y = x.