Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function, switching the roles of inputs and outputs.

Tags

CCSS.HSF-BF.B.4A

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, switch x and y, and solve for y.

Tags

CCSS.HSF-BF.B.4A

Front

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

Back

f^-1(x) = (x - 3)/2.

Tags

CCSS.HSF-BF.B.4A

Front

What does it mean to find the inverse of a function graphically?

Back

It means reflecting the graph of the function over the line y = x.

Tags

CCSS.HSF-BF.B.4C

Front

If f(x) = x^2, what is f^-1(x)?

Back

f^-1(x) = √x (for x ≥ 0).

Tags

CCSS.HSF-BF.B.4A

Front

What is the relationship between a function and its inverse?

Back

If f(g(x)) = x and g(f(x)) = x, then f and g are inverses.

Tags

CCSS.HSF-BF.B.4B

Front

What is the inverse of f(x) = -4x - 12?

Back

f^-1(x) = -1/4x - 3.

Tags

CCSS.HSF-BF.B.4A

Front

What does it mean to switch x's and y's in a function?

Back

It means to find the inverse function by interchanging the input and output values.

Tags

CCSS.HSF-BF.B.4A

Front

If f(x) = 3x + 10, what is g(f(x)) if g(x) = ⅓x - 3?

Back

None of these.

Tags

CCSS.HSF-BF.A.1C

Front

What is the line of reflection for inverse functions?

Back

The line of reflection is y = x.

Tags

CCSS.HSF-BF.B.4C