document.write( "Question 1066644: If f(-4)=5, which of the following could not be the inverse of f(x)?
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\n" ); document.write( "b)g(x)=x^2-11
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\n" ); document.write( "d)g(x)=-x^2+3x+6\r
\n" ); document.write( "\n" ); document.write( "Please help. My textbook doesn't have an example for a problem like this so I don't know where to even start. \n" ); document.write( "
Algebra.Com's Answer #681900 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "She is forgetting that only one-to-one functions can HAVE or BE \r\n" );
document.write( "inverse functions. These are functions  which pass both the \r\n" );
document.write( "horizontal and vertical line tests.  No 2nd degree polynomial \r\n" );
document.write( "functions are one-to-one, because they have u-shaped graphs \r\n" );
document.write( "(parabolas) which do not pass the horizontal line test (unless\r\n" );
document.write( "their domain is restricted.\r\n" );
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document.write( "So b), c), and d) are not one-to-one functions, and are immediately\r\n" );
document.write( "eliminated.  The only possibility is a).  But let's see why.\r\n" );
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document.write( "f(-4)=5 means this: \r\n" );
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document.write( "When -4 is substituted for x in f(x), the result is 5.\r\n" );
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document.write( "Then in order for g(x) to be the inverse of f(x), then g(x)\r\n" );
document.write( "must be a one-to-one function and we have the vice-versa of\r\n" );
document.write( "the above.  That is:\r\n" );
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document.write( "when 5 is substituted for x in the right side of g(x), the result\r\n" );
document.write( "must be -4.\r\n" );
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document.write( "a) g(x)=x-9\r\n" );
document.write( "   g(5)=5-9 = -4\r\n" );
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document.write( "So (a) is the correct answer.\r\n" );
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document.write( "Notice that choices c) and d) might trick a student into thinking\r\n" );
document.write( "they are correct because you also get -4 when you substitute x=5\r\n" );
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document.write( "c)g(5)=5^2-5(5)-4 = 25-25-4 = -4\r\n" );
document.write( "d)g(5)=-5^2+3(5)+6 = -25+15+6 = -4\r\n" );
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document.write( "But they are not one-to-one functions because a u-shaped graph cannot \r\n" );
document.write( "pass the horizontal line test.\r\n" );
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document.write( "Edwin
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