document.write( "Question 1180065: g(x) = 3x+4, determine n such that g(-3) = g^-1(n): \n" ); document.write( "

Algebra.Com's Answer #809651 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( " $\"g%28x%29+=+3x%2B4\"$ \r
\n" ); document.write( "\n" ); document.write( " determine $\"n\"$ such that $\"g%28-3%29+=+g%5E-1%28n%29\"$ \r
\n" ); document.write( "\n" ); document.write( "first find $\"g%5E-1%28x%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"g%28x%29+=+3x%2B4\"$ ......replace $\"g%28x%29+\"$ with $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=+3x%2B4\"$ .....swap variables\r
\n" ); document.write( "\n" ); document.write( " $\"x=+3y%2B4\"$ ........solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x-4=+3y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"y=x%2F3-4%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( "=> $\"g%5E-1%28x%29=x%2F3-4%2F3\"$ => it will be $\"g%5E-1%28x%29=+g%5E-1%28n%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "now find $\"g%28-3%29+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"g%28-3%29+=+3%28-3%29%2B4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"g%28-3%29+=+-9%2B4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"g%28-3%29+=+-5\"$ \r
\n" ); document.write( "\n" ); document.write( "then find
\n" ); document.write( " $\"g%5E-1%28n%29=-5\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-5=n%2F3-4%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-5%2B4%2F3=n%2F3\"$ ...both sides multiply by $\"3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-15%2B4=n\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"n=-11\"$ \r
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