document.write( "Question 933421: Please help me solve theses problems: Let f(x)= x^2+2 and g(x)=x+1\r
\n" ); document.write( "\n" ); document.write( "a)f(2)=
\n" ); document.write( "b)g(x)=7
\n" ); document.write( "c)f(g(3))=
\n" ); document.write( "d)g(f(x))=
\n" ); document.write( "e) f^-1(x)= \n" ); document.write( "

Algebra.Com's Answer #566798 by MathLover1(20850) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"f%28x%29=+x%5E2%2B2\"$ and $\"g%28x%29=x%2B1\"$ \r
\n" ); document.write( "\n" ); document.write( "a) $\"f%282%29\"$ =\r
\n" ); document.write( "\n" ); document.write( " $\"f%282%29=+2%5E2%2B2\"$
\n" ); document.write( " $\"f%282%29=+4%2B2\"$
\n" ); document.write( " $\"f%282%29=+6\"$ \r
\n" ); document.write( "\n" ); document.write( "b) $\"g%28x%29=7\"$
\n" ); document.write( " $\"7=x%2B1\"$
\n" ); document.write( " $\"7-1=x\"$
\n" ); document.write( " $\"6=x\"$ \r
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\n" ); document.write( "\n" ); document.write( "c) $\"f%28g%283%29%29\"$ =
\n" ); document.write( "first find $\"g%283%29\"$
\n" ); document.write( " $\"g%283%29=3%2B1\"$
\n" ); document.write( " $\"g%283%29=4\"$ ...plug it in for $\"x\"$ in $\"f%28x%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%284%29=+4%5E2%2B2\"$
\n" ); document.write( " $\"f%284%29=16%2B2\"$
\n" ); document.write( " $\"f%284%29=18\"$ \r
\n" ); document.write( "\n" ); document.write( "or
\n" ); document.write( " $\"f%28g%283%29%29=%28x%2B1%29%5E2%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28g%283%29%29=%283%2B1%29%5E2%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28g%283%29%29=4%5E2%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28g%283%29%29=16%2B2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28g%283%29%29=18\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "d) $\"g%28f%28x%29%29\"$ =\r
\n" ); document.write( "\n" ); document.write( " $\"g%28f%28x%29%29=x%5E2%2B2%2B1\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"g%28f%28x%29%29=x%5E2%2B3\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "e) $\"f%5E-1%28x%29\"$ =\r
\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=+x%5E2%2B2\"$ ....since $\"f%28x%29=+y\"$ we have\r
\n" ); document.write( "\n" ); document.write( " $\"y=+x%5E2%2B2\"$ ...swap $\"x\"$ and $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x=+y%5E2%2B2\"$ ...solve for $\"y\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"x-2=+y%5E2\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"sqrt%28x-2%29=+y\"$ \r
\n" ); document.write( "\n" ); document.write( "so, $\"f%5E-1%28x%29\"$ =ą $\"sqrt%28x-2%29%29\"$ \r
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