document.write( "Question 1073536: Given that g(x)=4/x , x is not equal to 0 and fg(x)=2x+3 find the function f.\r
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Algebra.Com's Answer #688342 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "I am looking in your post and CAN NOT understand, what is your fg(x) = 2x +3 ?\r
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\n" ); document.write( "\n" ); document.write( "Is it fog(x) (composition) ?\r
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\n" ); document.write( "\n" ); document.write( "Or (fg)(x) (the product of the two functions) ?\r
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\n" ); document.write( "\n" ); document.write( "Could you clarify ?\r
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\n" ); document.write( "Comment from student: composition.
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\n" ); document.write( "\n" ); document.write( "My responce. OK, composition.\r
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document.write( "1.  First of all, it means that your original formulation in the post was wrong.\r\n" );
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document.write( "    The correct writing is  fog(x)=2x+3.\r\n" );
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document.write( "    The composition is always denoted as fog.\r\n" );
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document.write( "2.  Then you can write fog(x) = f(g(x)) =  = 2x + 3.\r\n" );
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document.write( "    Replace here  by other variable, for example, t.\r\n" );
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document.write( "    You will get f(t) = 2x + 3.\r\n" );
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document.write( "    But since t = , you have x = , therefore\r\n" );
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document.write( "    f(t) =  = .\r\n" );
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document.write( "    Now you can replace t in both sides by x (it is simply another symbol for the variable), and you will get f(x) = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "It is your answer: f(x) = $\"8%2Fx+%2B+3\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Check. fog(x) = f(g(x) = $\"f%284%2Fx%29\"$ = $\"%288%2F%28%284%2Fx%29%29%29+%2B+3\"$ = $\"%288x%29%2F4%2B3\"$ = 2x + 3. Correct !\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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