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

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, then solve for y.

Tags

CCSS.HSF-BF.B.4A

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f^-1(x), which is read as 'f inverse of x'.

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

If f(a) = b, what is f^-1(b)?

Back

f^-1(b) = a.

Tags

CCSS.HSF-BF.B.4C

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

Front

What is the range of an inverse function?

Back

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

Tags

CCSS.HSF-BF.B.4C

Front

How can you verify if two functions are inverses?

Back

To verify, 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 inverse of the function f(x) = 2x + 3?

Back

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

Tags

CCSS.HSF-BF.B.4A

Front

What is the inverse of the function f(x) = x^2 (for x ≥ 0)?

Back

f^-1(x) = √x.

Tags

CCSS.HSF-BF.B.4D