Question

Given () = { 1, ≥ 0 2, < 0 . Is () continuous? Justify your answer.

Answer 1

Step-by-step explanation:

The given function is f(x)=5x−3

At x=0,f(0)=5(0)−3=−3

x→3limf(x)=x→3limf(5x−3)=5(0)−3=−3

∴x→3limf(x)=f(0)

Therefore, f is continuous at x=0

At x=−3,f(−3)=5(−3)−3=−18

x→−3limf(x)=x→−3lim(5x−3)=5(−3)−3=−18

∴x→−3limf(x)=f(−3)

Therefore, f is continuous at x=−3

At x=5,f(x)=f(5)=5(5)−3=25−3=22

x→5limf(x)=x→5lim(5x−3)=5(5)−3=22

∴ x→5limf(x)=f(5)

Therefore, f is continuous at x