inverse functions
Operations that reverse
Inverse functions are mathematical functions that reverse each other's operations.
If one function transforms input A into output B, its inverse transforms B back into A.
The functions "undo" each other: applying both in sequence returns you to where you started.
The inverse function of squaring is taking the square root.
Not all functions have inverses—a function must be one-to-one, with each output coming from exactly one input.
Exactly paired correspondence
composition · mapping · invertible · correspondence · permutation · isomorphism · restriction · ordered pair
Returned light or thought
- symmetryInvariance under transformation
- flipQuick turning motion
- undoingCause of destruction
- switchingChanging from one to another
transposition · interchange · mirror · axis · rotation · backtracking · cancellation · restoration
Function's rate of change
- antiderivativeReverse of differentiation
- integrationCombining into a whole
- differentiationRecognizing meaningful differences
- chain ruleComposite function derivative method
continuity · arcsine · arccosine · arctangent · natural logarithm · slope · tangent line · fixed point
Splitting into parts
- fractionPart divided by whole
- denominatorFraction's bottom number
- numeratorNumber being divided
- ratioComparative numerical relation
one-to-one
Exactly paired correspondence
image · composition · mapping · invertible · correspondence · permutation · isomorphism · restriction · ordered pair
reflection
Returned light or thought
switching · transposition · interchange · mirror · axis · rotation · backtracking · cancellation · restoration
derivative
Function's rate of change
- antiderivativeReverse of differentiation
- integrationCombining into a whole
- differentiationRecognizing meaningful differences
chain rule · continuity · arcsine · arccosine · arctangent · natural logarithm · slope · tangent line · fixed point · iteration
division
Splitting into parts
- fractionPart divided by whole
- denominatorFraction's bottom number
- numeratorNumber being divided
ratio · reciprocity · determinant · singular · Gaussian elimination
- trigonometrysine, cosine, tangent, secant, cosecant
- mathematical functionslogarithm, absolute value, square root, tangent, secant
- precalculuspolynomials, trigonometry, logarithms, domain, range
- Calculatorspocket calculator, scientific calculator, graphing calculator, basic calculator, desk calculator
- algebravariables, equations, equation, polynomials, algebraic equations
- complex analysiscomplex numbers, modulus, complex plane, analytic, singularity