document.write( "Question 1179408: if g(x) = 3x+4, determine n such that g(-3)=g^-1(n) \n" ); document.write( "

Algebra.Com's Answer #808959 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "if $\"g%28x%29+=+3x%2B4\"$ , determine $\"n\"$ such that $\"g%28-3%29=g%5E-1%28n%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"g%28x%29+=+3x%2B4\"$ \r
\n" ); document.write( "\n" ); document.write( "then\r
\n" ); document.write( "\n" ); document.write( " $\"g%28-3%29=3%2A%28-3%29%2B4\"$
\n" ); document.write( " $\"g%28-3%29=-5\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "now find $\"g%5E-1%28x%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"g%28x%29+=+y\"$ \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( " $\"g%5E-1%28x%29=x%2F3-4%2F3\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "since $\"g%28-3%29=g%5E-1%28n%29=-5\"$ and $\"g%5E-1%28x%29=x%2F3-4%2F3\"$ , replace $\"x\"$ with $\"n\"$ , then we have\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"g%5E-1%28n%29=n%2F3-4%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-5=n%2F3-4%2F3\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-15=n-4\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"-15%2B4=n\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"n=-11\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "check:\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"g%5E-1%28-11%29=-11%2F3-4%2F3=-5\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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