document.write( "Question 939682: determine if g is the inverse of f.\r
\n" ); document.write( "\n" ); document.write( "http://i.imgur.com/nCQxKGv.png\r
\n" ); document.write( "\n" ); document.write( "f(x)=4 + x^2,x≥0; g(x)=√x - 4 \n" ); document.write( "

Algebra.Com's Answer #572705 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( " $\"f%28x%29=4+%2B+x%5E2\"$ , $\"x%3E=0\"$ ; $\"g%28x%29=sqrt%28x-4%29\"$ \r
\n" ); document.write( "\n" ); document.write( "find inverse:\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=4+%2B+x%5E2\"$ ......... $\"f%28x%29=y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=4+%2B+x%5E2\"$ ..........swap $\"x\"$ and $\"y\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x=4+%2B+y%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x-4=y%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=sqrt%28x-4%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"f%5E-1%28x%29=sqrt%28x-4%29\"$ for $\"x%3E=0\"$ \r
\n" ); document.write( "\n" ); document.write( "so, $\"g%28x%29=sqrt%28x-4%29\"$ in inverse $\"f%28x%29=4+%2B+x%5E2\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+4+%2B+x%5E2%2C+sqrt%28x-4%29%29+\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );