- #1
ATCG
- 17
- 0
Could somebody please explain to me how you would calulate the inverse functions of x^3+4x+1. And if possible how you would calulate that on the TI-83 graphing calculator. Thanks
Calculating Inverse Functions for Cubic Equations: A Guide for TI-83 Users
- Thread starter ATCG
- Start date
In summary, the conversation is about calculating the inverse functions of x^3+4x+1 and whether or not it can be done using a TI-83 graphing calculator. The expert notes that the exact formula for the inverse would require the cubic formula, which is complicated and not typically used in class. They suggest finding another way to solve the problem. The person asking for help then confirms that they have found the cubic formula and asks for assistance. The expert expresses curiosity about the original problem.
- #2
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
- 14,981
- 26
You don't.
The exact formula for the inverse of this function requries the cubic formula, which is fairly complicated (although in this case the result is readable), and is almost certainly not what you are expected to do in class; there's probably a way to find the answer to your problem without having to explicitly compute this inverse.
- #3
ATCG
- 17
- 0
It is expected. If you know how to solve this equation please tell me.
- #4
Hurkyl
Staff Emeritus
Science Advisor
Gold Member
- 14,981
- 26
I see you've found the cubic formula. 
Do you still need help with it?
I'm curious what the actual text of the problem is.
Do you still need help with it?I'm curious what the actual text of the problem is.
1. What is an inverse function?
An inverse function is a function that reverses the effect of another function. In other words, if a function f(x) maps an input x to an output y, then the inverse function f^-1(y) maps the output y back to the original input x. Inverse functions are commonly used in mathematics and science to solve equations and analyze relationships between variables.
2. How do I find the inverse of a function?
To find the inverse of a function, you can follow these steps:
- Write the function as y = f(x).
- Switch the x and y variables, so the equation becomes x = f(y).
- Solve the new equation for y in terms of x.
- The resulting equation is the inverse function of the original function.
3. Are all functions invertible?
No, not all functions have an inverse. For a function to be invertible, it must pass the horizontal line test, meaning that every horizontal line intersects the graph of the function at most once. If a function fails this test, it does not have a unique inverse.
4. How do inverse functions relate to logarithms?
Inverse functions and logarithms are closely related. Logarithms are the inverse functions of exponential functions, and they are used to solve equations involving exponential functions. The logarithm of a number is the exponent to which another fixed value (the base) must be raised to produce that number. For example, log base 10 of 100 is 2, because 10^2 = 100.
5. Why are inverse functions important?
Inverse functions are important because they allow us to solve equations and analyze relationships between variables in a wide range of fields, including mathematics, physics, and engineering. They also help us understand the behavior of functions and their graphs, and they have practical applications in fields such as finance and computer science.
Similar threads
-
General Math
-
General Math
-
Linear and Abstract Algebra
-
General Math
-
General Math
-
Precalculus Mathematics Homework Help
-
General Math
-
General Math