document.write( "Question 1121072: Show that the mapping f:R-R be defined by f(x) = ax + b where a,b € R, a is not equal to 0 is invertible, define its inverse \n" ); document.write( "

Algebra.Com's Answer #737023 by rothauserc(4718) $\"\"$ $\"About$

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R together with the binary operation +, forms a Group.
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\n" ); document.write( "This means that R is closed under +, ax+b is an element in G, say c and c has an inverse(-c) such that c +(-c) = identity element(e) = 0
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\n" ); document.write( "f(x) = ax +b
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\n" ); document.write( "let y = f(x) then
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\n" ); document.write( "y = ax +b
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\n" ); document.write( "interchange the x and y, then solve for y
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\n" ); document.write( "x = ay +b
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\n" ); document.write( "y = (x -b) / a
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\n" ); document.write( "therefore,
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\n" ); document.write( "the inverse of f(x) = (x -b)/a
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