We have to prove that given any ε>0 we can find a δε>0 such that
∣f(x)−1∣<ε∀x∈(2−δε,2+δε)
Let's evaluate the difference
∣f(x)−1∣=∣3x−5−1∣=∣3x−6∣=3∣x−2∣
Therefore
∣f(x)−1∣<ε⇔∣x−2∣<3ε
Given, that ε>0 we can choose δε<3ε
Hence
x∈(2−δε,2+δε)⇒∣x−2∣<3ε⇔∣f(x)−1∣<ε
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