Which functions are continuous at x=-4?

Hence, functions in options (b) and (d) are continuous at x= -4.

Step-by-step explanation:

A function f(x) is continuous at x=a; if the left hand limit(L.H.L) at a=right hand limit (R.H.L.) at a=f(a).

(a)

We are given function f(x) as:

            when x≠ -4

and f(x)=0 when x= -4

L.H.L at x= -4    is f(x)= -8  ( since limit x→ -4 f(x)= -8 (as -4-4= -8))

R.H.L. at x=-4  is f(x)= -8

Also f(-4)=0

hence function f(x) is not continuous at x= -4. ( since L.H.L=R.H.L.≠f(-4) )

(b)

We are given function f(x) as:

    when x≠ -4

and f(x)= -8 when x≠ -4.

Clearly as in part (1)

L.H.L at x= -4    is f(x)= -8  ( since limit x→ -4 f(x)= -8 (as -4-4= -8))

R.H.L. at x=-4  is f(x)= -8

Also f(-4)= -8.

Hence, the function f(x) is continuous  ( since L.H.L=R.H.L.=f(-4) )

(c)

We are given function f(x) as:

when x≠-4

and f(x)=16 when x= -4

L.H.L. at x= -4  is 0  ( since limit x→ -4 f(x)=0 (as -4+4=0) )

R.H.L. at x= -4 is 0.

f(-4)= 16

Hence, the function f(x) is not continuous. ( since L.H.L=R.H.L.≠f(-4) )

(d)

We are given function f(x) as:

when x≠-4

and f(x)=0 when x= -4

L.H.L. at x= -4  is 0  ( since limit x→ -4 f(x)=0 (as -4+4=0) )

R.H.L. at x= -4 is 0.

f(-4)= 0

Hence, the function f(x) is  continuous. ( since L.H.L=R.H.L.=f(-4) )

nlgqer

step-by-step