document.write( "Question 1210395: What is the inverse of Y=(X+3)² ? \n" ); document.write( "

Algebra.Com's Answer #852194 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "What is the inverse of Y=(X+3)² ?
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document.write( "The direct function (which is the given function) does the following:\r\n" );
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document.write( "    - it adds the number 3 to the argument and then squares the value.\r\n" );
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document.write( "Therefore, the range of the given function is the set of all non-negative real numbers.\r\n" );
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document.write( "It means that the domain of the inverse function is the set of all non-negative real  numbers,\r\n" );
document.write( "and at this set the inverse function makes the opposite operations in reverse order:\r\n" );
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document.write( "    - first, it takes square root from the value, and after that subtract 3 from the square root.\r\n" );
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document.write( "So, we can write an expression for the inverse function\r\n" );
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document.write( "    g(x) =  - 3.\r\n" );
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document.write( "But square root from a real number can be positive or negative.\r\n" );
document.write( "Therefore, there are TWO possible expressions for \"the\" inverse function.\r\n" );
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document.write( "First  expression is  p(x) =  - 3,   using positive value of .\r\n" );
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document.write( "Second expression is  q(x) = - - 3,  using negative value of . \r\n" );
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document.write( "These two possible expressions define two possible inverse functions.\r\n" );
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document.write( "Both inverse functions are defined over the set of non-negative real numbers.\r\n" );
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document.write( "First inverse function has the range [,).\r\n" );
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document.write( "Second inverse function has the range (-,].\r\n" );
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\n" ); document.write( "\n" ); document.write( "At this point, the problem is solved completely, with detailed explanations, so everybody can understand.\r
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\n" ); document.write( "\n" ); document.write( "It is important to note that the question in the problem is not precisely correct/accurate.\r
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\n" ); document.write( "\n" ); document.write( "Indeed, it asks   \" what is the inverse function of Y = $\"%28X%2B3%29%5E2\"$ ?\"\r
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\n" ); document.write( "\n" ); document.write( "To be correct, in this situaion, the question should ask   \" what are possible inverse functions of Y = $\"%28X%2B3%29%5E2\"$ ?\"\r
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\n" ); document.write( "\n" ); document.write( "        Now, after reading my post, you are armed to the teeth:
\n" ); document.write( "        you know the right question and also know the right answer.\r
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\n" ); document.write( "\n" ); document.write( "Come again to this forum soon to learn something new from the best source.\r
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