<PRE><B>Question 1188984</B>
&lt;br&gt;
(1) A standard algebraic method for finding the inverse of a function: switch the variables and solve for the new y.&lt;br&gt;
Given: {{{y=23/x^2}}}&lt;br&gt;
Switch variables:&lt;br&gt;
{{{x=23/y^2}}}&lt;br&gt;
Solve for y:&lt;br&gt;
{{{y^2=23/x}}}
{{{y=sqrt(23/x)}}}&lt;br&gt;
(2) An informal method, using the idea that an inverse function &quot;un-does&quot; what the function does.&lt;br&gt;
The given function does the following to the input:&lt;br&gt;
square it; take the reciprocal; multiply by 23&lt;br&gt;
{{{x}}} --&gt; {{{x^2}}} --&gt; {{{1/x^2}}} --&gt; {{{23/x^2}}}&lt;br&gt;
The inverse function must do the opposite operations, in the opposite order:&lt;br&gt;
divide by 23; take the reciprocal; take the square root&lt;br&gt;
{{{x}}} --&gt; {{{x/23}}} --&gt; {{{23/x}}} --&gt; {{{sqrt(23/x)}}}&lt;br&gt;
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