Inverse of a function

Front

What is the definition of the inverse of a function?

Back

The inverse of a function is a function that reverses the mapping of the original function, such that if the original function maps an input x to an output y, the inverse function maps y back to x.

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method used to determine if a curve is a function. If any vertical line intersects the curve at more than one point, the curve is not a function.

Front

What is the Horizontal Line Test?

Back

The Horizontal Line Test is a method used to determine if a function has an inverse that is also a function. If any horizontal line intersects the graph of the function at more than one point, the function does not have an inverse that is a function.

Front

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

Back

A function is one-to-one if it assigns a unique output to each input, meaning no two different inputs produce the same output.

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 in the equation and solve for y.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is the significance of the mapping diagram in understanding functions?

Back

A mapping diagram visually represents how each input is paired with an output, helping to clarify the relationship between the two.

Front

What is the relationship between a function and its inverse?

Back

The relationship is such that if f(x) = y, then f-inverse(y) = x. The inverse function undoes the action of the original function.

Front

Provide an example of a one-to-one function.

Back

An example of a one-to-one function is f(x) = 2x + 3, where each input x produces a unique output.