document.write( "Question 1199261: Given f(x)= x^3+x+4, find the f^-1(1) accurate to two decimal places \n" ); document.write( "

Algebra.Com's Answer #833051 by ikleyn(52750) $\"\"$ $\"About$

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\n" ); document.write( "Given f(x)= x^3+x+4, find the f^-1(1) accurate to two decimal places
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document.write( "Left side is a monotonic function of x on the entire number line (over all real numbers),\r\n" );
document.write( "because the derivative function 3x^2 + 1 is positive everywhere.\r\n" );
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document.write( "Therefore, the inverse function f^-1(x) does exist and is defined over all number line, too.\r\n" );
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document.write( "To find the value f^-1(x), it is enough to solve equation\r\n" );
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document.write( "    x^3 + x + 4 = 1,  or,  equivalently,  x^3 + x + 3 = 0.\r\n" );
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document.write( "I used online free of charge solver https://www.mathportal.org/calculators/solving-equations/polynomial-equation-solver.php\r\n" );
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document.write( "Below is the solution produced by the solver.\r\n" );
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document.write( "x1 = −1.21341\r\n" );
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document.write( "x2 = 0.60671 + 1.45061*i\r\n" );
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document.write( "x3 = 0.60671 − 1.45061*i\r\n" );
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document.write( "Explanation\r\n" );
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document.write( "This polynomial has no rational roots that can be found using Rational Root Test.\r\n" );
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document.write( "Roots were found using cubic formulas.\r\n" );
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document.write( "So, the unique real value/root/solution is  x = −1.21,  rounded to two decimal places.\r\n" );
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