document.write( "Question 51335: Given the functions $\"f%28x%29+=+6x%5E2+-+8x+-+23\"$ and $\"g%28x%29+=+27+-+9x\"$ . Find each of the following:
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\n" ); document.write( " g(-4)
\n" ); document.write( " f(-4)
\n" ); document.write( " f(5 + h) - f(5) \n" ); document.write( "

Algebra.Com's Answer #34358 by rchill(405) $\"\"$ $\"About$

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The notation g(-4) means we take \"-4\" and substitute it in the g() function anywhere there is \"x\". So, $\"g%28-4%29+=+27-9%2A%28-4%29+=+27-%28-36%29+=+27%2B36+=+63\"$ . Similarly, for function f(), we get

. We do the same for $\"f%285+%2B+h%29+-+f%285%29\"$ , but have to call the f() function twice: once for (5+h) and the other for (5). Solving f(5+h) produces $\"6%285%2Bh%29%5E2+-+8%285%2Bh%29+-+23\"$ which simplifies to $\"6%2A%28h%5E2%2B10h%2B25%29+-40-8h-23\"$ , which further simplifies to $\"6h%5E2%2B60h%2B150-40-8h-23\"$ . Combining like terms produces $\"6h%5E2%2B52h%2B87\"$ . Because we solved f(5) earlier to get $\"f%285%29=87\"$ , we can now solve $\"f%285+%2B+h%29+-+f%285%29\"$ by substitution: $\"6h%5E2%2B52h%2B87-87\"$ which simplifies to $\"6h%5E2%2B52h\"$ , which can be rewritten as $\"2h%2A%283h%2B26%29\"$ . \n" ); document.write( "

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