Prove that {x-1, when1≤x<2,2x-3 when 2≤x≤3 is continuous at x=2

Question

Prove that  \(f(x) = \begin{cases} x-1, & \quad \text{when 1 ≤x<2;} \text{}\\ 2x-3, & \quad \text{when 2 ≤x≤3} \end{cases}\)  is continuous at x = 2

Answer 1

f(x)=2x-3 [this equation is taken as equality for x=1 lies there] f(2)= 1 

Since,  \(\lim\limits_{x \to2} \) f(x) = f(2) 

f is continuous at x=2.