ApplySides [f,rel]
applies f to each side of the equation or inequality rel.
ApplySides
ApplySides [f,rel]
applies f to each side of the equation or inequality rel.
Details
- The relations rel can have any of the following forms:
-
lhs==rhs equationslhs!=rhs inequationslhs>rhs or lhs>=rhs inequalitiesab>c≥… generalized inequalities
- ApplySides does not verify that inequalities are still valid after function application.
Examples
open all close allBasic Examples (2)
Exponentiate both sides of an equation:
ApplySides[Exp, Log[x] == 2]Take the square root of both sides of an inequality:
ApplySides[Sqrt, x ^ 2 + 1 > 4]Scope (6)
Compute the logarithm of each side of an equation with three expressions:
ApplySides[Log, a == b^2 == c^3]Take the cube root of each side of a generalized inequality:
ApplySides[CubeRoot, a == b > -8 > c]Apply Factorial to both sides of an inequation:
ApplySides[Factorial, n ≠ 5]Raise each side of an equation to the fourth power using a pure function:
ApplySides[# ^ 4&, a == I b]Apply Sinh to several inequalities expressed using Piecewise :
ApplySides[Sinh, Piecewise[{{x^2 > c/a + (b*x)/a, a > 0}, {x^2 < c/a + (b*x)/a, a < 0}}, a*x^2 > c + b*x]]Compute the common logarithm of both sides of an equation inside ConditionalExpression :
ApplySides[Log10, ConditionalExpression[(a/c) == (b/d), c ≠ 0]]Applications (1)
Derive the quadratic formula:
quadratic = a x^2 + b x + c == 0Multiply both sides by 4 a:
MultiplySides[quadratic, 4a, Assumptions -> a ≠ 0]//ExpandAdd b^2-4 a c to both sides:
AddSides[%, b^2 - 4a c]Factor the left-hand side:
Factor[%]Take the positive square root of both sides:
ApplySides[Sqrt, %]Cancel the square root of the square:
PowerExpand[%]Subtract b from both sides:
SubtractSides[%, b]Divide both sides by 2 a to obtain the quadratic formula for x with positive square root:
DivideSides[%, 2a, Assumptions -> a ≠ 0]Properties & Relations (2)
True and False are considered trivial equations:
ApplySides[Sin, True]ApplySides[Cos, 1 == 0]ApplySides transforms equations to related equations:
ApplySides[Exp, Log[x] == 5]Solve gives values for the variables that make the equation true:
Solve[Log[x] == 5, x]Reduce can be used to rewrite an equation in the form var==value:
Reduce[Log[x] == 5, x]Possible Issues (1)
ApplySides is a purely structural operation and does not check mathematical consistency:
ApplySides[Sin, x > c]The new inequality is not equivalent to the original:
{x > c, Sin[x] > Sin[c]} /. {x -> 3Pi / 2, c -> Pi / 2}Related Guides
History
Text
Wolfram Research (2018), ApplySides, Wolfram Language function, https://reference.wolfram.com/language/ref/ApplySides.html.
CMS
Wolfram Language. 2018. "ApplySides." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ApplySides.html.
APA
Wolfram Language. (2018). ApplySides. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ApplySides.html
BibTeX
@misc{reference.wolfram_2026_applysides, author="Wolfram Research", title="{ApplySides}", year="2018", howpublished="\url{https://reference.wolfram.com/language/ref/ApplySides.html}", note=[Accessed: 14-August-2026]}
BibLaTeX
@online{reference.wolfram_2026_applysides, organization={Wolfram Research}, title={ApplySides}, year={2018}, url={https://reference.wolfram.com/language/ref/ApplySides.html}, note=[Accessed: 14-August-2026]}