document.write( "Question 1194819: Determine analytically, if the function 𝑓, whose correspondence rule is 𝑓(𝑥) = 𝑥^3
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Algebra.Com's Answer #827085 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "given: $\"f%28x%29+=+x%5E3\"$ \r
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\n" ); document.write( "\n" ); document.write( "To show that a function is $\"injective\"$ , we assume that there are elements $\"a\"$ and $\"b\"$ of a domain with $\"f%28a%29+=+f%28b%29\"$ and then show that $\"a+=+b\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"f%28a%29=f%28b%29\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28a%29=a%5E3+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"f%28b%29=b%5E3+\"$ \r
\n" ); document.write( "\n" ); document.write( " $\"a%5E3=b%5E3\"$ take the cubic root of each side\r
\n" ); document.write( "\n" ); document.write( " $\"a=b\"$ \r
\n" ); document.write( "\n" ); document.write( "Therefore, $\"f\"$ is $\"injective\"$ .\r
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