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.

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.

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.

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].

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.

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.

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.

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.

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.