Inverse 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 back to x.

Tags

CCSS.HSF-BF.B.4A

Front

If f(g(x)) = x, what can we conclude about f and g?

Back

f and g are inverses of each other only if f(g(x)) = x for all x in the domain of g.

Tags

CCSS.HSF-BF.B.4B

Front

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

Back

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

Tags

CCSS.HSF-BF.B.4A

Front

How do you find the inverse of a function graphically?

Back

To find the inverse graphically, reflect the graph of the function over the line y = x.

Tags

CCSS.HSF-BF.B.4C

Front

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

Back

The coordinates of a function and its inverse are swapped. If (a, b) is on f(x), then (b, a) is on f⁻¹(x).

Tags

CCSS.HSF-BF.B.4C

Front

What is the inverse of the coordinates (1, 2), (3, 8), (-3, 6)?

Back

The inverse coordinates are (2, 1), (8, 3), (6, -3).

Tags

CCSS.HSF-BF.B.4C

Front

TRUE or FALSE: The inverse of f(x) = x² is g(x) = √(x).

Back

FALSE. The inverse is not a function because it fails the vertical line test for negative values.

Front

What points does f⁻¹(x) go through if f(x) goes through (1, 4) and (4, 6)?

Back

f⁻¹(x) goes through (4, 1) and (6, 4).

Tags

CCSS.HSF-BF.B.4C

Front

What line do inverse functions reflect over?

Back

Inverse functions reflect over the line y = x.

Tags

CCSS.HSF-BF.B.4C

Front

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

Back

The notation for the inverse of a function f(x) is f⁻¹(x).