Question

Prove that the function f(x) = 5x – 3 is continuous at x = 0, at x = –3 and at x = 5.

Answer 1

The given function is:

f(x) = 5x – 3

f(0) = 5(0) – 3 = –3

`lim_(x → 0)` f(x) = 5(0) – 3 = –3

`lim_(x → 0)` f(x) = f(0)

Hence, the function is continuous at x = 0.

f(–3) = 5(–3) – 3

= –15 – 3

= –18

⇒ `lim_(x → -3)` f(x) = 5(–3) – 3

= –15 – 3

= –18

⇒ `lim_(x → -3)` f(x) = f(–3)

Hence, the function is continuous at x = –3.

f(5) = 5(5) – 3

= 25 – 3

= 22

⇒ `lim_(x → 5)` f(x)

= 5(5) – 3

= 25 – 3

= –22

⇒ `lim_(x -> 5)` f(x) = f(5)

Hence, the function is continuous at x = 5.