1. What is an Inverse Function?

An inverse function reverses the operation of the original function. If f(x) = y, then the inverse function f⁻¹(y) = x. The calculator finds the input x that produces a given output y.

2. How Does the Calculator Work?

The calculator uses algebraic manipulation to solve for x:

Where:

• \( y \) — Output value of the original function
• \( f(x) \) — Original function expression
• \( x \) — Input value that produces the output y

Explanation: The calculator algebraically manipulates the equation y = f(x) to solve for x in terms of y.

3. Importance of Inverse Functions

Details: Inverse functions are fundamental in mathematics for reversing operations, solving equations, and understanding mathematical relationships. They have applications in physics, engineering, and computer science.

4. Using the Calculator

Tips: Enter the function expression using standard mathematical notation (e.g., 2*x+3, x^2, sin(x)). Provide the output value y that you want to find the corresponding input for.

5. Frequently Asked Questions (FAQ)

Q1: What types of functions can this calculator handle?
A: The calculator can handle linear, polynomial, exponential, logarithmic, and trigonometric functions, among others.

Q2: What if a function doesn't have an inverse?
A: For a function to have an inverse, it must be one-to-one. The calculator will indicate if an inverse cannot be found for the given function.

Q3: How accurate are the results?
A: Results are mathematically exact for functions that have algebraic solutions. For more complex functions, numerical methods are used.

Q4: Can I use variables other than x?
A: The calculator uses x as the default variable. For functions with other variables, you may need to adapt your input.

Q5: What mathematical notation should I use?
A: Use * for multiplication, ^ for exponents, and standard function names (sin, cos, tan, log, ln, etc.).