Question 4 [7]
Prove that 𝑓(𝑥) = 𝑥^2 + 2𝑥 is not injective.
Since 𝑓(0)=02+2⋅0=0𝑓(0) = 0^2 + 2\cdot 0=0f(0)=02+2⋅0=0 and 𝑓(−2)=(−2)2+2(−2)=4−4=0,𝑓(-2) = (-2)^2 + 2(-2)=4-4=0,f(−2)=(−2)2+2(−2)=4−4=0,we conclude that f(0)=f(−2),f(0)=f(-2),f(0)=f(−2), and hence fff is not injective.
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