document.write( "Question 1015265: let f(x)=1+1/x^2, find a function y=g(x) so that f(g(x))=x \n" ); document.write( "
Algebra.Com's Answer #631633 by Edwin McCravy(20060)\"\" \"About 
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document.write( "let \"f%28x%29=1%2B1%2Fx%5E2\", find a function \"y=g%28x%29\" so that \"f%28g%28x%29%5E%22%22%29=x\"\r\n" );
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document.write( "Substitute y for x in the right side of f(x) and set it equal to x,\r\n" );
document.write( "and solve for y:\r\n" );
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document.write( "\"1%2B1%2Fy%5E2\"\"%22%22=%22%22\"\"x\"\r\n" );
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document.write( "\"1%2Fy%5E2\"\"%22%22=%22%22\"\"x-1\"\r\n" );
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document.write( "Take reciprocals of both sides:\r\n" );
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document.write( "\"y%5E2\"\"%22%22=%22%22\"\"1%2F%28x-1%29\"\r\n" );
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document.write( "Take positive square roots of both sides:\r\n" );
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document.write( "\"y\"\"%22%22=%22%22\"\"g%28x%29\"\"%22%22=%22%22\"\"1%2Fsqrt%28x-1%29\"\r\n" );
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document.write( "------------------\r\n" );
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document.write( "Checking to see if \"f%28g%28x%29%5E%22%22%29=x\":\r\n" );
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document.write( "\"f%28g%28x%29%5E%22%22%29\"\"%22%22=%22%22\"\"f%281%2Fsqrt%28x-1%29%29\"\"%22%22=%22%22\"\"1\"\"%22%22%2B%22%22\"\"matrix%282%2C1%2C%22%22%2C%281%5B%22%22%5D%29%2F%28%281%2Fsqrt%28%28x-1%29%29%29%5E2%29%29\"\"%22%22=%22%22\"\r\n" );
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document.write( "\"1\"\"%22%22%2B%22%22\"\"matrix%282%2C1%2C%22%22%2C%281%5B%22%22%5D%29%2F%28%281%2F%28x-1%29%29%29%29\"\"%22%22=%22%22\"\"1%2B%28x-1%29\"\"%22%22=%22%22\"\"1%2Bx-1\"\"%22%22=%22%22\"\"x\"\r\n" );
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document.write( " Edwin

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