<h1 id="inverse">Inverse<a aria-hidden="true" class="anchor-heading icon-link" href="#inverse"></a></h1>
An inverse function undoes the operation of the original function.
<ul>
<li>that is, the inverse function of a function f (also called the inverse of f) is a function that undoes the operation of f.</li>
</ul>
ex. imagine we have a function
<div class="math math-display"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mn>5</mn><mi>x</mi><mo>−</mo><mn>7</mn></mrow><annotation encoding="application/x-tex">f(x) = 5x − 7</annotation></semantics></math>f(x)=5x−7</div>
One can think of <math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>f</mi></mrow><annotation encoding="application/x-tex">f</annotation></semantics></math>f as "the function which multiplies its input by 5 then subtracts 7 from the result". To undo this, one adds 7 to the input, then divides the result by 5.
Therefore, the inverse is
<div class="math math-display"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mi>y</mi><mo>+</mo><mn>7</mn><mo stretchy="false">)</mo><mi mathvariant="normal">/</mi><mn>5</mn></mrow><annotation encoding="application/x-tex">f(y) = (y + 7)/5</annotation></semantics></math>f(y)=(y+7)/5</div>
<h3 id="celsius-fahrenheit">Celsius-Fahrenheit<a aria-hidden="true" class="anchor-heading icon-link" href="#celsius-fahrenheit"></a></h3>
Consider that the inverse of the formula to calculate C to F is the same formula to calculate F to C.
<div class="math math-display"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>C</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>9</mn><mrow><mn>5</mn><mi>C</mi></mrow></mfrac><mo>+</mo><mn>32</mn></mrow><annotation encoding="application/x-tex">f(C) = {9\over5C} + 32</annotation></semantics></math>f(C)=5C9​+32</div>
<div class="math math-display"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>F</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>5</mn><mn>9</mn></mfrac><mo stretchy="false">(</mo><mi>F</mi><mo>−</mo><mn>32</mn><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">f(F) = {5\over9}(F - 32)</annotation></semantics></math>f(F)=95​(F−32)</div>
Therefore, <code>f(F)</code> is the inverse of <code>f(C)</code>, and <code>f(C)</code> is the inverse of <code>f(F)</code>
<hr>
Backlinks
<ul>
<li><a href="/notes/TBATXjmhVgnvCDmR1mVuD">Calculus</a></li>
<li><a href="/notes/axBYWAH6oBhlGDw3ZbEdY">Logarithm</a></li>
</ul>

Inverse

thoughts-on


Welcome to my Second Brain! Here you'll find thoughts, lessons, facts and any other interesting musings that I've come across or thought up over the years. A lot of what I have gathered is originally from the minds of others, while some of it originates from myself. Some notes may contain misinformation, though I try to be rigorous with my additions.

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