Question

If function is defined by { f(x) = 1 - x if x < -1 r2 if x>-1 Evaluatef(-2)​

Answer 1

Answer:

as {f(x) = 1-x

we have to find out f(-2)

then put x=2

so,f(-2)= 1-(-2) =3.

hence f(2)= -3.

Answer 2

Solution

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The given function is

f(x)={

x,ifx≤1

5,ifx>1

At x=0

It is evident thatf is defined at 0 and its value at 0 is 0.

Then

x→0

lim

f(x)=

x→0

lim

x=0

∴

x→0

lim

f(x)=f(0)

Therefore, f is continuous at x=0

At x=1,

f is defined at 1 and its value at 1 is 1.

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

x→1

lim

f(x)=

x→1

lim

x=1

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

x→1

lim

f(x)=

x→1

lim

(5)=5

∴

x→1

lim

f(x)



=

x→1

lim

f(x)

Therefore, f is not continuous at x=1.

At x=2,

f is defined at 2 and its value at 2 is 5.

Then,

x→2

lim

f(x)=

x→2

lim

(5)=5

∴

x→2

lim

f(x)=f(2)

Therefore, f is continuous at x=2