Find the inverse of a function and Piecewise Functions

Front

What is the definition of an inverse function?

Back

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

Front

How do you find the inverse of a function algebraically?

Back

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

Front

What is the graphical representation of a function and its inverse?

Back

The graph of a function and its inverse are symmetric with respect to the line y = x.

Front

What is a piecewise function?

Back

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the domain.

Front

How do you determine if a function has an inverse?

Back

A function has an inverse if it is one-to-one, meaning it passes the horizontal line test.

Front

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

Back

A function is one-to-one if each output value corresponds to exactly one input value.

Front

How can you find the inverse of a piecewise function?

Back

To find the inverse of a piecewise function, find the inverse of each piece separately and ensure the ranges match the original domains.

Front

What is the significance of the points (a, b) and (b, a) in relation to inverse functions?

Back

If (a, b) is a point on the function f, then (b, a) will be a point on its inverse f^-1.

Front

What is the process to verify if two functions are inverses of each other?

Back

To verify if two functions are inverses, check if f(f^-1(x)) = x and f^-1(f(x)) = x for all x in the domain.

Front

What is the domain of an inverse function?

Back

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