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Question
Let A = {–1, 1} and B = {0, 2}. If the function f: A → B defined by f(x) = ax + b is an onto function? Find a and b
Solution
A = {–1, 1}; B = {0, 2}
f(x) = ax + b
f(–1) = a(–1) + b
0 = –a + b
a – b = 0 ….(1)
f(1) = a(1) + b
2 = a + b
a + b = 2 ….(2)
Solving (1) and (2) we get
a – b = 0 ....(1)
a + b = 2 ....(2)
(1) + (2) ⇒ 2a = 2
a = `(2)/(2)` = 1
Substitute a = 1 in (1)
The value of a = 1 and b = 1
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