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