Inverse Functions - with graphs

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 find the inverse of a function given its graph?

Back

To find the inverse of a function from its graph, reflect the graph over the line y = x.

Front

What is the relationship between a function and its inverse?

Back

A function and its inverse are symmetric with respect to the line y = x.

Front

Are the functions f(x) = 2x + 3 and g(x) = (x - 3)/2 inverses of each other?

Back

Yes, they are inverses because f(g(x)) = x and g(f(x)) = x.

Front

What is the inverse of the coordinates (1, 2)?

Back

The inverse is (2, 1).

Front

If a function is not one-to-one, can it have an inverse?

Back

No, a function must be one-to-one (each output has a unique input) to have an inverse.

Front

What is the inverse of the function f(x) = x² for x ≥ 0?

Back

The inverse is f⁻¹(x) = √x.

Front

How do you determine if two functions are inverses?

Back

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

Front

What is the inverse of the points (2, 5), (3, 7)?

Back

The inverse points are (5, 2), (7, 3).

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.