SOLUTION: 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

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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
Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
R together with the binary operation +, forms a Group.
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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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f(x) = ax +b
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let y = f(x) then
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y = ax +b
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interchange the x and y, then solve for y
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x = ay +b
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y = (x -b) / a
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therefore,
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the inverse of f(x) = (x -b)/a
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