document.write( "Question 1177905: For each of the following, determine if the function is increasing, decreasing, even, odd, and/or invertible on its natural domain:
\n" ); document.write( "f(x) = sqrt{x-5}
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Algebra.Com's Answer #807048 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( " $\"f%28x%29+=+sqrt%28x-5%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "if $\"f\"$ ’ > $\"0\"$ the function is increasing
\n" ); document.write( "if $\"f\"$ ’ < $\"0\"$ the function is increasing\r
\n" ); document.write( "\n" ); document.write( " $\"f\"$ ’ $\"%28x%29+=+1%2F%282+sqrt%28x+-+5%29%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f\"$ ’ > $\"0\"$ for $\"x%3E5\"$
\n" ); document.write( " $\"f\"$ ’ < $\"0\"$ -> no solution in $\"x\"$ element $\"R\"$ \r
\n" ); document.write( "\n" ); document.write( "the function is increasing $\"5%3Cx%3Cinfinity\"$ \r
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\n" ); document.write( "\n" ); document.write( " A function is even if $\"f%28-x%29=f%28x%29\"$ for all $\"x\"$ element $\"R\"$ .
\n" ); document.write( " $\"f%28-x%29=f%28x%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"+sqrt%28-x-5%29=sqrt%28x-5%29\"$
\n" ); document.write( " $\"-x-5%3C%3E++x-5\"$ => A function is $\"not\"$ even\r
\n" ); document.write( "\n" ); document.write( "A function is odd if $\"f%28-x%29=-f%28x%29\"$ for all $\"x\"$ element $\"R\"$ .\r
\n" ); document.write( "\n" ); document.write( " $\"f%28-x%29=f%28x%29+\"$
\n" ); document.write( " $\"sqrt%28-x-5%29=-+sqrt%28x-5%29\"$
\n" ); document.write( " $\"-x-5%3C%3E+-%28x-5%29\"$
\n" ); document.write( " $\"-x-5%3C%3E+-x%2B5\"$ => A function is $\"not\"$ odd\r
\n" ); document.write( "\n" ); document.write( "so, your function is $\"neither\"$ $\"+even\"$ $\"+nor\"$ $\"+odd\"$ \r
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\n" ); document.write( "\n" ); document.write( "If $\"y+=+f+%28x%29\"$ , then the inverse relation is written as $\"y+=+f+%5E-1%28x%29\"$ .
\n" ); document.write( " $\"If+\"$ the $\"inverse\"$ is also a $\"function\"$ , then we say that the function $\"f\"$ is $\"invertible\"$ .\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29+=+sqrt%28x-5%29\"$ ...find inverse
\n" ); document.write( " $\"f%28x%29+=+y\"$
\n" ); document.write( " $\"y+=+sqrt%28x-5%29\"$ ....swap $\"x\"$ and $\"y\"$
\n" ); document.write( " $\"x+=+sqrt%28y-5%29\"$ ........solve for $\"y\"$ , square both sides
\n" ); document.write( " $\"x%5E2+=y-5\"$
\n" ); document.write( " $\"x%5E2%2B5+=y\"$
\n" ); document.write( " $\"f+%5E-1%28x%29=x%5E2%2B5\"$ which is also a $\"function\"$ \r
\n" ); document.write( "\n" ); document.write( "so, $\"f%28x%29+=+sqrt%28x-5%29\"$ is $\"invertible\"$ on its natural domain\r
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