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, replace f(x) with y, swap x and y, and then solve for y. The resulting equation is the inverse function.

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 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 inverse of the coordinates (4, 5)?

Back

The inverse is (5, 4).

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 does it mean if a function is one-to-one?

Back

A one-to-one function means that each output is produced by exactly one input, allowing for an inverse to exist.

Front

What is the inverse of f(x) = x² for x ≥ 0?

Back

f^-1(x) = √x.

Tags

CCSS.HSF-BF.B.4D

Front

What is the first step to find the inverse of f(x) = 3x - 5?

Back

Replace f(x) with y: y = 3x - 5.

Tags

CCSS.HSF-BF.B.4A