Question

prove that the function is continues f(x)=5x-3

Answer 1

The given function is f(x)=5x−3

At x=0,f(0)=5(0)−3=−3

x→3

lim

f(x)=

x→3

lim

f(5x−3)=5(0)−3=−3

∴

x→3

lim

f(x)=f(0)

Therefore, f is continuous at x=0

At x=−3,f(−3)=5(−3)−3=−18

x→−3

lim

f(x)=

x→−3

lim

(5x−3)=5(−3)−3=−18

∴

x→−3

lim

f(x)=f(−3)

Therefore, f is continuous at x=−3

At x=5,f(x)=f(5)=5(5)−3=25−3=22

x→5

lim

f(x)=

x→5

lim

(5x−3)=5(5)−3=22

∴

x→5

lim

f(x)=f(5)

Therefore, f is continuous at x=5.

Hence f is continuous at all the given points (In fact f is continuous for all R, Since it is a polynomial )