document.write( "Question 381052: f(x)=-2+log[4](x-3)how do you find the inverse. \n" ); document.write( "
Algebra.Com's Answer #270377 by jsmallt9(3758)\"\" \"About 
You can put this solution on YOUR website!
To find an inverse:
  1. If function notation is present, replace it with a \"y\".
  2. Rewrite the equation \"swapping\" the x's and y's. IOW, where there is an \"x\" replace it with a \"y\" and where there is a \"y\" replace it with an \"x\". This actually changes the equation. The new equation is the inverse relation for the previous equation. But it is not in the desired form, yet.
  3. Solve the inverse equation for y, if possible.
    • If it is possible to solve for y and if function notation was used initially, then replace the \"y\" with f-1(x).
    • If it is not possible to solve for y, then the inverse relation is not a function.

\n" ); document.write( "Let's see this in action:
\n" ); document.write( "\"f%28x%29=-2%2Blog%284%2C+%28x-3%29%29\"
\n" ); document.write( "1) Replace f(x) with y:
\n" ); document.write( "\"y=-2%2Blog%284%2C+%28x-3%29%29\"
\n" ); document.write( "2) Swap the x's and y's:
\n" ); document.write( "\"x=-2%2Blog%284%2C+%28y-3%29%29\"
\n" ); document.write( "3) Solve for y:
\n" ); document.write( "\"x+%2B+2+=+log%284%2C+%28y-3%29%29\"
\n" ); document.write( "Rewrite in exponential form:
\n" ); document.write( "\"4%5E%28x+%2B+2%29+=+y-3\"
\n" ); document.write( "\"4%5E%28x+%2B+2%29%2B3+=+y\"
\n" ); document.write( "We solved for y and we have function notation initially so we will replace y:
\n" ); document.write( "\"4%5E%28x+%2B+2%29%2B3\" = f-1(x) \n" ); document.write( "
\n" );