Question

11.Examine the continuity of the function f(x)=1/x+3​

Answer 1

Answer:

We have f(x)=2x

2

−1

At x=3,f(x)=f(3)=2(3)

2

−1=17

and

x→3

lim

f(x)=

x→3

lim

(2x

2

−1)=2(3)

2

−1=17

Clearly

x→3

lim

f(x)=f(3)

Thus, f is continuous at x=3.

Answer 2

Answer:

Step-by-step explanation:

f(x) = 1/x+3

As x+3 is denominator ,

x+3≠0

x≠-3

And x∈R includes all real numbers

Therefore, function is discontinuous at x=-3 and hence not continuous for x∈R.

Thank you ….