document.write( "Question 1169488: what is the inverse function of y=3x^3-9 including steps? \n" ); document.write( "
Algebra.Com's Answer #794264 by math_helper(2461)\"\" \"About 
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\n" ); document.write( "\"+y+=+3x%5E3-9+\"\r
\n" ); document.write( "\n" ); document.write( "General strategy: solve for x then swap x & y at the very end.\r
\n" ); document.write( "\n" ); document.write( "\"+y%2B9+=+3x%5E3+\" <--- added 9 to both sides
\n" ); document.write( "\"+%28y%2B9%29%2F3+=+x%5E3+\" <--- divided both sides by 3
\n" ); document.write( "\"+root%283%2C%28%28y%2B9%29%2F3%29%29+=+x+\" <--- took cube root of both sides\r
\n" ); document.write( "\n" ); document.write( "\"+x+=+root%283%2C%28%28y%2B9%29%2F3%29%29+\" <--- re-wrote w/x on left hand side\r
\n" ); document.write( "\n" ); document.write( "Now swap x & y:
\n" ); document.write( "\"+highlight%28+y+=+root%283%2C+%28%28x%2B9%29%2F3%29%29+%29+\" <--- this is the inverse function\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Check...
\n" ); document.write( "You can check it by computing \"+f%5E-1%28f%28x%29%29+\" ... it should give you x back.
\n" ); document.write( "We plug in '\"+%283x%5E3-9%29+\"' for 'x' in the inverse function:
\n" ); document.write( " (ok) \n" ); document.write( "
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