Inverse Function Calculator
Find the inverse of functions with step-by-step solutions
Solution Steps
Inverse Function Calculator – Find Function Inverses Instantly
Our advanced inverse function calculator helps you find the inverse of various function types with step-by-step solutions. Perfect for students and professionals working with algebraic, exponential, logarithmic, and trigonometric functions.
How to Use the Calculator
- Enter your function in the input field (e.g., 2x+3, e^x, log(x))
- Select the appropriate variable and function type
- Use the math keypad for special symbols
- Click calculate to get the inverse function
- Review the step-by-step solution process
What is an Inverse Function?
An inverse function reverses the operation of the original function. Key properties:
- Denoted as f⁻¹(x)
- f(f⁻¹(x)) = x and f⁻¹(f(x)) = x
- Only exists for bijective functions
- Graph is reflection of original function over y=x line
Common Inverse Function Types
| Function Type | Example | Inverse |
|---|---|---|
| Linear | f(x) = 2x + 3 | f⁻¹(x) = (x-3)/2 |
| Exponential | f(x) = e^x | f⁻¹(x) = ln(x) |
| Logarithmic | f(x) = log(x) | f⁻¹(x) = 10^x |
| Trigonometric | f(x) = sin(x) | f⁻¹(x) = arcsin(x) |
Key Features
- Supports multiple function types
- Step-by-step solutions
- Variable selection
- Mathematical symbol keypad
- Error checking system
- Mobile-friendly design
Frequently Asked Questions
Can all functions be inverted?
Only bijective functions (both injective and surjective) have true inverses. Some functions require domain restrictions.
How do you verify inverse functions?
Verify that f(f⁻¹(x)) = x and f⁻¹(f(x)) = x for all x in the appropriate domains.
What’s the inverse of a quadratic function?
Quadratic functions require domain restrictions. For f(x) = x² (x ≥ 0), the inverse is f⁻¹(x) = √x.
Can I find inverses of trigonometric functions?
Yes, but they require specific domain restrictions. For example, sin⁻¹(x) has domain [-1, 1] and range [-π/2, π/2].
Bookmark this inverse function calculator for quick access to reliable mathematical solutions. Essential tool for algebra, calculus, and advanced mathematics courses!