Inverse Relations and Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) = y, then the inverse function f⁻¹(y) = x.

Tags

CCSS.HSF-BF.B.4A

Front

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

Back

Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Tags

CCSS.HSF-BF.B.4B

Front

What is the relationship between the domain of a function and the range of its inverse?

Back

The domain of a function becomes the range of its inverse, and the range of the function becomes the domain of its inverse.

Tags

CCSS.HSF-BF.B.4A

Front

What is the range of the inverse function if the original function has a range of [3, ∞)?

Back

The range of the inverse function will be (-∞, 3].

Tags

CCSS.HSF-BF.B.4C

Front

What does it mean for two graphs to be inverses?

Back

Two graphs are inverses if they are reflections of each other over the line y = x.

Tags

CCSS.HSF-BF.B.4B

Front

If a function is defined as f(x) = 2x + 3, what is its inverse?

Back

The inverse function is f⁻¹(x) = (x - 3)/2.

Tags

CCSS.HSF-BF.B.4A

Front

What is the significance of the line y = x in relation to inverse functions?

Back

The line y = x serves as the line of reflection for the graphs of a function and its inverse.

Tags

CCSS.HSF-BF.B.4B

Front

Can a function have more than one inverse?

Back

No, a function can have only one inverse if it is a one-to-one function.

Tags

CCSS.HSF-BF.B.4D

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, ensuring that it has an inverse.

Front

How do you find the inverse of a function graphically?

Back

To find the inverse graphically, reflect the graph of the function over the line y = x.

Tags

CCSS.HSF-BF.B.4C