Inverse of Cubic Function
Steps to find the inverse of the cubic function are:
Step 1: Write the cubic function as y = f(x).
Step 2: Swap the places of ‘x’ and ‘y’
Step 3: Simplify and solve for ‘y’ if possible.
Step 4: Obtained value of y is the inverse of the cubic function.
Inverse of the cube function is the cube root function i.e., for f(x) = x3,
f-1(x) = ∛x
For Example: Find the inverse of the cubic function f(x) = x3 + 2.
Solution:
Let y = f(x) = x3 + 2
Now, Swap the places of ‘x’ and ‘y’
x = y3 + 2
⇒ y3 = x – 2
⇒ y = ∛(x – 2)
Since y = f-1(x)
f-1(x) = ∛(x – 2)
So, the inverse of given cubic function is ∛(x – 2).
Cubic Function
A cubic function is a polynomial function of degree 3 and is represented as f(x) = ax3 + bx2 + cx + d, where a, b, c, and d are real numbers and a ≠ 0. Cubic functions have one or three real roots and always have at least one real root. The basic cubic function is f(x) = x3
Let’s learn more about the Cubic function, its domain and range, asymptotes, intercepts, critical and inflection points, and others along with some detailed examples in this article.
Table of Content
- What is Cubic Function?
- Roots of Cubic Function
- Intercepts of a Cubic Function
- Graph of Cubic Function
- Characteristics of Cubic Function
- Inverse of Cubic Function
- Extrema of Cubic Function
- End Behavior of Cube Function
- Graphing Cubic Function
- Cubic Function Vs Quadratic Function
- Examples on Cubic Functions