document.write( "Question 995514: Suppose f(x)=ax^4+bx^2+x+5, where a and b are constants. Find f(4) if f(-4)=3 \n" ); document.write( "

Algebra.Com's Answer #614259 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Suppose f(x)=ax^4+bx^2+x+5, where a and b are constants. Find f(4) if f(-4)=3.
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\n" ); document.write( "\n" ); document.write( "Let us write the fact that f(-4) = 3.\r
\n" ); document.write( "\n" ); document.write( "Simply substitute x = -4 into the given polynomial. You will have\r
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\n" ); document.write( "\n" ); document.write( "f(-4) = $\"a%2A%28-4%29%5E4+%2B+b%2A%28-4%29%5E2+%2B+%28-4%29+%2B+5\"$ = $\"3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Simplify it, taking into account that $\"%28-4%29%5E4\"$ = $\"4%5E4\"$ and $\"%28-4%29%5E2\"$ = $\"4%5E2\"$ . You will have \r
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\n" ); document.write( "\n" ); document.write( "f(-4) = $\"a%2A4%5E4+%2B+b%2A4%5E2+%2B+%28-4%29+%2B+5\"$ = $\"3\"$ . (1) \r
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\n" ); document.write( "\n" ); document.write( "Now express f(4). Simply substitute x = 4 into the given polynomial. You will get \r
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\n" ); document.write( "\n" ); document.write( "f(4) = $\"a%2A4%5E4+%2B+b%2A4%5E2+%2B+4+%2B+5\"$ . (2) \r
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\n" ); document.write( "\n" ); document.write( "Now compare expressions (1) and (2). They are almost identical. The difference is in linear terms (-4) in (1) and 4 in (2). \r
\n" ); document.write( "\n" ); document.write( "Hence, f(4) is in 8 units greater than f(-4). It means that f(4) = f(-4) + 8 = 3 + 8 = 11.\r
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\n" ); document.write( "\n" ); document.write( "Answer. f(4) = 11.\r
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