document.write( "Question 107683: State the domain of the following:
\n" ); document.write( "
\n" ); document.write( "g(x)=2x+1/x-3
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #78443 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
a \"function\" must be $\"single-valued+\"$ which means \"one and only one\"; to each value of $\"x+\"$ there is a $\"unique\"$ value of $\"y\"$ .\r
\n" ); document.write( "\n" ); document.write( "The values that $\"x\"$ may assume are called the $\"domain\"$ of the function, and those are the values for which the function is $\"defined\"$ .
\n" ); document.write( "In the function $\"+y+=+ax+%2B+b\"$ , the $\"domain\"$ may include $\"all+\"$ $\"real\"$ $\"+numbers+\"$ ; consequently, $\"x\"$ could be $\"any\"$ $\"+real\"$ $\"+number\"$ . \r
\n" ); document.write( "\n" ); document.write( "But, there is $\"one\"$ case in which the domain $\"must\"$ be restricted, and that is the case when a denominator $\"may\"$ $\"+not\"$ $\"+be\"$ $\"+0\"$ . \r
\n" ); document.write( "\n" ); document.write( "So, in this function $\"g%28x%29=%282x%2B1%29%2F%28x-3%29\"$ a denominator $\"x-3\"$ may not be equal to $\"0\"$ because to divide by $\"0\"$ doesn’t make a sense.\r
\n" ); document.write( "\n" ); document.write( "Let set it equal to $\"0\"$ in order to find what $\"x\"$ may not be in a domain:\r
\n" ); document.write( "\n" ); document.write( " $\"x-3+=+0\"$
\n" ); document.write( " $\"x+=+0+%2B3\"$
\n" ); document.write( " $\"x+=+3\"$ \r
\n" ); document.write( "\n" ); document.write( "Solution:\r
\n" ); document.write( "\n" ); document.write( "In a domain could be all other real numbers except $\"3\"$ .\r
\n" ); document.write( "\n" ); document.write( "Domain: ( $\"-+infinity\"$ , $\"3\"$ ] and [ $\"3\"$ , $\"%2Binfinity\"$ )
\n" ); document.write( " \n" ); document.write( "

\n" );