Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) = y, then the inverse function f⁻¹(y) = x.

Tags

CCSS.HSF-BF.B.4A

Front

How can you determine if two functions are inverses of each other?

Back

You can determine if two functions are inverses by composing them. If f(g(x)) = x and g(f(x)) = x, then they are inverses.

Tags

CCSS.HSF-BF.B.4B

Front

What is the horizontal line test?

Back

The horizontal line test is a method to determine if a function has an inverse. If any horizontal line intersects the graph of the function more than once, the function does not have an inverse.

Front

What does it mean if a function passes the horizontal line test?

Back

If a function passes the horizontal line test, it means that it is one-to-one and has an inverse function.

Front

What is the composition of functions?

Back

The composition of functions is the process of applying one function to the results of another. It is denoted as (f ∘ g)(x) = f(g(x)).

Tags

CCSS.HSF-BF.A.1C

Front

What is the significance of the composition of functions in determining inverses?

Back

The composition of functions helps verify if two functions are inverses. If f(g(x)) = x and g(f(x)) = x, then they are inverses.

Tags

CCSS.HSF-BF.B.4B

Front

What is a radical function?

Back

A radical function is a function that contains a variable within a radical (square root, cube root, etc.). For example, f(x) = √x or f(x) = ∛x.

Front

What is a cubic function?

Back

A cubic function is a polynomial function of degree three, typically in the form f(x) = ax³ + bx² + cx + d, where a ≠ 0.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse of a function algebraically, swap the x and y in the equation and solve for y.

Tags

CCSS.HSF-BF.B.4A

Front

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

Back

The graphs of a function and its inverse are reflections of each other across the line y = x.

Tags

CCSS.HSF-BF.B.4C