Question

The function f(x) = 5x – 3 is continuous at x =

Options

• 0

• – 3

• Both 0 and – 3

• Neither 0 nor – 3

Answer 1

Both 0 and – 3

Explanation:

At `x` = 0, `lim_(x -> 0), f(x)`

= `lim_(x -> 0) (5x - 3)` = – 3

And `f(0)` = – 3

∴ `f` is continuous at `x` = 0 

At `x` = – 3, `lim_(x -> -3) f(x) = lim_(x -> -3) (5x - 3)` = – 18

`f(-3)` = – 18

∴ `f` is continuous at `x` = – 3