document.write( "Question 1196880: If f(x+1)-7=f(x), find f(x) \n" ); document.write( "

Algebra.Com's Answer #829907 by ikleyn(52776) $\"\"$ $\"About$

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\n" ); document.write( "If f(x+1)-7 = f(x), find f(x).
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document.write( "If  f(x+1)-7 = f(x), it implies that\r\n" );
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document.write( "    f(x+1) = f(x) + 7.      (1)\r\n" );
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document.write( "If consider \"x\" as a variable in integer numbers (as an \"index\"), then equation (1)\r\n" );
document.write( "defines an arithmetic progression with the common difference 7.\r\n" );
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document.write( "Had a value of f(x) be given in the problem for some integer value of x, \r\n" );
document.write( "then equation (1) would determine the progression in a UNIQUE way.\r\n" );
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document.write( "But since the value of f(x) is not given in the problem for some x, \r\n" );
document.write( "we can say nothing more about this arithmetic progression.\r\n" );
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document.write( "There are infinitely many arithmetic progressions described by this formula.\r\n" );
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document.write( "If consider \"x\" as a variable in real numbers (a continuous variable), then equation (1)\r\n" );
document.write( "defines a straight line  with the slope of 7:   = 7.\r\n" );
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document.write( "Had a value of f(x) be given in the problem for some real value of x, \r\n" );
document.write( "then it would determine the straight line in a UNIQUE way.\r\n" );
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document.write( "But since f(x) is not given in the problem for some x, there are infinitely many \r\n" );
document.write( "such straight lines described by this equation (with the slope 7).\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, answered and explained.\r
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\n" ); document.write( "\n" ); document.write( "That is all what Math can tell you about f(x) defined by the given equation.\r
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\n" ); document.write( "\n" ); document.write( "With the given information in the post, it is IMPOSSIBLE \" to find f(x) \".\r
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\n" ); document.write( "\n" ); document.write( "What is only possible is to determine a class (or a type) of a sequence f(x)
\n" ); document.write( "(as an arithmetic progression in discrete case) or a function f(x) (as a linear function).\r
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\n" ); document.write( "\n" ); document.write( "So, if to understand each word literally in the post, this post is not SELF-CONSISTENT:
\n" ); document.write( "it requires to do something, that can not be done.\r
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