3-2 Verifying Inverses of 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 verify if two functions are inverses?

Back

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

Front

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

Back

The graph of a function and its inverse are reflections of each other across the line y = x.

Front

What does it mean if two functions are not inverses?

Back

If two functions are not inverses, it means that applying one function after the other does not return the original input.

Front

What is the significance of the horizontal line test?

Back

The horizontal line test determines if a function is one-to-one. If any horizontal line intersects the graph more than once, the function does not have an inverse.

Front

Can a function have more than one inverse?

Back

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

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 no two different inputs map to the same output.

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f⁻¹(x), where f is the original function.

Front

How can you find the inverse of a function algebraically?

Back

To find the inverse of a function algebraically, swap the x and y variables and solve for y.

Front

What is the domain of an inverse function?

Back

The domain of the inverse function is the range of the original function.