# Is the function f defined by f(x) = {(x, if x ≤ 1), (5, if x > 1) continuous at x = 0? At x = 1? At x = 2?

**Solution:**

The given function is

f(x) = {(x, if x ≤ 1) (5, if x > 1)

At x = 0,

It is evident that f is defined at 0 and its value at 0 is 0.

Then,

lim_{x→0} f(x) = lim_{x→0} (x) = 0

⇒ lim_{x→0} f(x) = f(0)

Therefore, f is continuous at x = 0.

At x = 1,

It is evident that f is defined at 1 and its value at 1 is 1.

The left hand limit of f at x = 1 is,

lim_{x→1−} f(x )= lim_{x→1−} (x) = 1

The right hand limit of f at x = 1 is,

lim_{x→1+} f(x) = lim_{x→1+} (5) = 5

⇒ lim_{x→1−} f(x) ≠ lim_{x→1+} f(x)

Therefore, f is not continuous at x = 1.

At x = 2,

It is evident that f is defined at 2 and its value at 2 is 5.

lim_{x→2} f(x) = lim_{x→2} (5) = 5

⇒ lim_{x→1} f(x) = f(2)

Therefore, f is continuous at x = 2

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

## Is the function f defined by f(x) = {(x, if x ≤ 1), (5, if x > 1) continuous at x = 0? At x = 1? At x = 2?

**Summary:**

For the given function f defined by f(x) = {(x, if x ≤ 1), (5, if x > 1)is continuous at x = 0.f is not continuous at x = 1.f is continuous at x = 2