document.write( "Question 262565: how to find the inverse of f(x)= sqrt((x^2)+8x) thanks :) \n" ); document.write( "

Algebra.Com's Answer #193412 by drk(1908) $\"\"$ $\"About$

You can put this solution on YOUR website!
here is the original equation:
\n" ); document.write( " $\"f%28x%29=+sqrt%28%28x%5E2%29%2B8x%29\"$
\n" ); document.write( "let f(x) = y and then reverse all x and y variables to get
\n" ); document.write( " $\"x=+sqrt%28%28y%5E2%29%2B8y%29\"$
\n" ); document.write( "step 1 - square both sides to get
\n" ); document.write( " $\"x%5E2+=+y%5E2+%2B+8y\"$
\n" ); document.write( "now x^2 is a constant, so we can set = 0 as
\n" ); document.write( " $\"y%5E2+%2B+8y+-+x%5E2+=+0\"$
\n" ); document.write( "using the quadratic formula, we get
\n" ); document.write( " $\"y+=+%28-8+%2B-+sqrt%2864+%2B+4%2A1%2Ax%5E2%29%29%2F2\"$
\n" ); document.write( "factor a 4 out of the sqrt to get
\n" ); document.write( " $\"y+=+%28-8+%2B-2sqrt%2816%2Bx%5E2%29%29%2F2\"$
\n" ); document.write( "reduce to get
\n" ); document.write( " $\"y%5E%28-1%29+=+%28-4+%2B-sqrt%2816%2Bx%5E2%29%29\"$ \n" ); document.write( "

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