2023 - 2024 - Cubic and Cube Root Test Review

Front

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

Back

The x's and y's are switched.

Front

Find the inverse: f(x) = x^3 - 1

Back

f^(-1)(x) = ∛(x + 1)

Front

What is the ONLY way to mathematically prove if two functions are inverses?

Back

FOG GOF.

Front

Solve for x; identify extraneous solutions (if any): x^3 - 3x - 8 = 0

Back

x = -42.

Front

Solve for x: (3x + 1)^3 = 64

Back

x = 1.

Front

What is a cube root?

Back

A cube root of a number x is a number y such that y^3 = x.

Front

How do you find the cube root of a number?

Back

Use the notation ∛x, which represents the cube root of x.

Front

What is the relationship between a function and its inverse?

Back

If f(x) is a function, then f^(-1)(f(x)) = x.

Front

What is the domain of a cube root function?

Back

The domain is all real numbers.

Front

What is the range of a cube root function?

Back

The range is all real numbers.