Q13 of 25 Page 1

Show that the function f: R → R, given by f(x) = ax + b, where a, b ∊ R, a ≠ 0 is a bijection.

Given: f(x) = ax + b


Check for one-one:


If f(x1) = f(x2)


ax1 + b = ax2 + b


x1 = x2


Therefore, the function is one-one.


Check for onto:


Let y = ax + b


for all y ∊ R(co-domain). Thus, for all y ∊ R (co-domain) there exists x ∊ R such that


f(x)


Therefore, the function is onto.


As the function is both one-one and onto, the given function is a bijection.


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