document.write( "Question 128610: Let $\"f%28x%29=3x\"$ , $\"g%28x%29=3x-3\"$ and $\"h%28x%29=%28f%2Ag%29%28x%29%2B%28f%2Fg%29%28x%29\"$ \r
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x f(x) g(x) h(x)
-1 -3
$\"1%2F3\"$ -2
12 $\"109%261%2F3\"$
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Algebra.Com's Answer #94090 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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x	f(x)	g(x)	h(x)
-1	-3
$\"1%2F3\"$		-2
	12		$\"109%26amp%3B1%2F3\"$

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\n" ); document.write( "\n" ); document.write( "Let's find the first entry of g(x)\r
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\n" ); document.write( "\n" ); document.write( " $\"g%28x%29=3x-3\"$ Start with the second function\r
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\n" ); document.write( "\n" ); document.write( " $\"g%28-1%29=3%28-1%29-3\"$ Plug in $\"x=1%2F3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"g%28-1%29=-3-3\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"g%28-1%29=-6\"$ Subtract\r
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\n" ); document.write( "\n" ); document.write( "So our table becomes\r
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x	f(x)	g(x)	h(x)
-1	-3	-6
$\"1%2F3\"$		-2
	12		$\"109%26amp%3B1%2F3\"$

\r
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\n" ); document.write( "\n" ); document.write( "Let's find the second entry of f(x)\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=3x\"$ Start with the first function\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%2F3%29=3%281%2F3%29\"$ Plug in $\"x=1%2F3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%2F3%29=3%2F3\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"f%281%2F3%29=1\"$ Reduce\r
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\n" ); document.write( "\n" ); document.write( "Now our table updates to\r
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x	f(x)	g(x)	h(x)
-1	-3	-6
$\"1%2F3\"$	1	-2
	12		$\"109%26amp%3B1%2F3\"$

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\n" ); document.write( "\n" ); document.write( "Let's find the third entry of x\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28x%29=3x\"$ Start with the first function\r
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\n" ); document.write( "\n" ); document.write( " $\"12=3x\"$ Plug in $\"f%28x%29=12\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"4=x\"$ Divide both sides by 3 to isolate x\r
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\n" ); document.write( "\n" ); document.write( " $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( "Now plug this value into the last row of the x column\r
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x	f(x)	g(x)	h(x)
-1	-3	-6
$\"1%2F3\"$	1	-2
4	12		$\"109%26amp%3B1%2F3\"$

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\n" ); document.write( "\n" ); document.write( "Let's find the third entry of g(x)\r
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\n" ); document.write( "\n" ); document.write( " $\"g%28x%29=3x-3\"$ Start with the second function\r
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\n" ); document.write( "\n" ); document.write( " $\"g%284%29=3%284%29-3\"$ Plug in $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"g%284%29=12-3\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"g%284%29=9\"$ Subtract\r
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x	f(x)	g(x)	h(x)
-1	-3	-6
$\"1%2F3\"$	1	-2
4	12	9	$\"109%261%2F3\"$

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\n" ); document.write( "\n" ); document.write( "Now let's find the first entry of h(x)\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28x%29=%28f%2Ag%29%28x%29%2B%28f%2Fg%29%28x%29\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28x%29=f%28x%29%2Ag%28x%29%2Bf%28x%29%2Fg%28x%29\"$ Break up the function\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28-1%29=f%28-1%29%2Ag%28-1%29%2Bf%28-1%29%2Fg%28-1%29\"$ Plug in $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"h%28-1%29=-3%2A%28-6%29%2B%28-3%29%2F%28-6%29\"$ Plug in $\"f%28-1%29=-3\"$ , $\"g%28-1%29=-6\"$ (these values are from the table)\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28-1%29=18%2B1%2F2\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28-1%29=37%2F2\"$ Add\r
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x	f(x)	g(x)	h(x)
-1	-3	-6	$\"37%2F2\"$
$\"1%2F3\"$	1	-2
4	12	9	$\"109%261%2F3\"$

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\n" ); document.write( "\n" ); document.write( "Now let's find the first entry of h(x)\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28x%29=%28f%2Ag%29%28x%29%2B%28f%2Fg%29%28x%29\"$ Start with the given function\r
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\n" ); document.write( "\n" ); document.write( " $\"h%28x%29=f%28x%29%2Ag%28x%29%2Bf%28x%29%2Fg%28x%29\"$ Break up the function\r
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\n" ); document.write( "\n" ); document.write( " $\"h%281%2F3%29=f%281%2F3%29%2Ag%281%2F3%29%2Bf%281%2F3%29%2Fg%281%2F3%29\"$ Plug in $\"x=1%2F3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"h%281%2F3%29=1%2A%28-2%29%2B%281%29%2F%28-2%29\"$ Plug in $\"f%281%2F3%29=1\"$ , $\"g%281%2F3%29=-2\"$ (these values are from the table)\r
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\n" ); document.write( "\n" ); document.write( " $\"h%281%2F3%29=-2-1%2F2\"$ Multiply and reduce\r
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\n" ); document.write( "\n" ); document.write( " $\"h%281%2F3%29=-5%2F2\"$ Combine the fractions\r
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x	f(x)	g(x)	h(x)
-1	-3	-6	$\"37%2F2\"$
$\"1%2F3\"$	1	-2	$\"-5%2F2\"$
4	12	9	$\"109%261%2F3\"$

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