Examine the continuity of the function f(x) = 2 x² − 1 at x = 3

Solution:

A function is said to be continuous when the graph of the function is a single unbroken curve.

The given function is

f(x) = 2 x² − 1

At x = 3,

f(3) = 2(3)² − 1

= 17

lim_x→3 f(x) = lim_x→3 (2 x² − 1)

= 2(3²) − 1 = 17

⇒ lim_x→3 f(x) = f(3)

Therefore,

f is continous at x = 3

NCERT Solutions Class 12 Maths - Chapter 5 Exercise 5.1 Question 2

Examine the continuity of the function f(x) = 2 x² − 1 at x = 3

Summary:

The continuity of the function f(x) = 2 x² − 1 at x = 3 is true.A function is said to be continuous when the graph of the function is a single unbroken curve