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
At x = 0, f(0) = 5x0-3 = 3
$\lim\limits_{x \to 0}$ f(x) = $\lim\limits_{x \to 0}$(5x-3) = 5x0-3 = -3
∴$\lim\limits_{x \to 0}$ f(x) = f(0)

Therefore,f is continuous at x=0

At x=-3, f(-3) = 5x(-3)-3 = -18
∴$\lim\limits_{x \to 0}$ = $\lim\limits_{x \to 3}$ (5x-3) = 5x(-3)-3 = -18
∴f(x) = f(-3)

Therefore, f is continuous at x=−3

At x=5, f(5) = 5x(5)-3 = 22
∴$\lim\limits_{x \to 5}$=$\lim\limits_{x \to 5}$ (5x-3) = 5x(5)-3= 22
∴f(x) = f(5)

Therefore, f is continuous at x = 5