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.

Tags

CCSS.HSF-BF.B.4A

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.

Tags

CCSS.HSF-BF.B.4A

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.

Tags

CCSS.HSF-BF.B.4C

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.

Tags

CCSS.HSF-BF.B.4D

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.

Tags

CCSS.HSF-BF.B.4C

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.

Tags

CCSS.HSF-BF.B.4B

Front

What is the domain of an inverse function?

Back

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

Tags

CCSS.HSF-BF.B.4C