Inverse Functions

Front

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

Back

The x's and y's are switched.

Tags

CCSS.HSF-BF.B.4A

Front

Given that f(x) = 3x + 5 and g(x) = 1/3x + 5, find f(g(x)). Are the two functions inverses of each other?

Back

f(g(x)) = x + 20; No, they are not inverses.

Tags

CCSS.HSF-BF.B.4B

Front

Find the inverse of f(x)=2x-2.

Back

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

Tags

CCSS.HSF-BF.B.4A

Front

What is the first step in finding the equation of the inverse of a function?

Back

Switch x and y.

Tags

CCSS.HSF-BF.B.4A

Front

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

Back

f^-1(x).

Front

If f(x) = x^2, what is the inverse function?

Back

f^-1(x) = √x (for x ≥ 0).

Tags

CCSS.HSF-BF.B.4A

Front

How do you verify if two functions are inverses of each other?

Back

Check if f(g(x)) = x and g(f(x)) = x.

Tags

CCSS.HSF-BF.B.4B

Front

What is the inverse of the function f(x) = 5x - 3?

Back

f^-1(x) = (x + 3)/5.

Tags

CCSS.HSF-BF.B.4A

Front

What happens to the domain of a function when you find its inverse?

Back

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

Tags

CCSS.HSF-BF.B.4C

Front

What is the graphical representation of inverse functions?

Back

They are reflections over the line y = x.

Tags

CCSS.HSF-BF.B.4C