Finding Inverses of Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y and produces 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 in the equation and solve for y.

Tags

CCSS.HSF-BF.B.4A

Front

What is the notation for the inverse of a function g(x)?

Back

The inverse of g(x) is denoted as g⁻¹(x).

Tags

CCSS.HSF-BF.B.4A

Front

What is the relationship between a function and its inverse?

Back

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

Tags

CCSS.HSF-BF.B.4C

Front

What does it mean for two functions to be inverses?

Back

Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Tags

CCSS.HSF-BF.B.4B

Front

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

Back

The inverse of the coordinates (1, 2) is (2, 1).

Tags

CCSS.HSF-BF.B.4C

Front

What is the inverse of the function f(x) = 3x + 2?

Back

To find the inverse, swap x and y: x = 3y + 2, then solve for y: f⁻¹(x) = (x - 2)/3.

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 the domain of a function's inverse?

Back

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

Tags

CCSS.HSF-BF.B.4C

Front

What is the range of a function's inverse?

Back

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

Tags

CCSS.HSF-BF.B.4C