Inverse Function Calculator
Function Type
Parameter a
Parameter b
✓Inverse Function
Original
f(x) = 2x + 3
Inverse f⁻¹(y)
f⁻¹(y) = (y − 3) / 2
The inverse function f⁻¹(x) undoes the effect of f(x). If f(a) = b, then f⁻¹(b) = a. Not every function has an inverse — it must be one-to-one (each output has exactly one input).
- 1Replace f(x) with y
- 2Swap x and y
- 3Solve for y — this is f⁻¹(x)
- 4Verify: f(f⁻¹(x)) = x and f⁻¹(f(x)) = x
f(x) = 2x + 3=f⁻¹(x) = (x−3)/2
f(x) = x³=f⁻¹(x) = x^(1/3) = ∛x
| f(x) | f⁻¹(x) | Domain of f⁻¹ |
|---|---|---|
| 2x+3 | (x−3)/2 | All reals |
| x² | √x | x≥0 |
| eˣ | ln(x) | x>0 |
| sin(x) | arcsin(x) | [−1,1] |
| 1/x | 1/x | x≠0 |
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