Math Is Fun Forum

ROBBYM

Member

Registered: 2008-04-24

Posts: 10

continuous

show the function f:R->R

when x does not equal 4
                        8 when x equals 4

is continuous on R

Last edited by ROBBYM (2008-04-27 19:28:42)

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: continuous

its not continuous, x cant take the value 4

ROBBYM

Member

Registered: 2008-04-24

Posts: 10

Re: continuous

So if i re-write it like this then

isn't this continuous if x does not equal 4

but if x equals 4  then f(x)=8 which is not continuous for all real values of x

therefore the function is not continuous????

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: continuous

The function is continuous. As you said, for x≠4 the function is equal to x+4. The function is defined piecewise, so you don't need to worry about division by 0 because it treats x=4 as a special case anyway.

As x gets close to 4, f(x) gets close to 4+4 = 8. f(4) is defined to be 8, and so there is no discontinuity at x=4. There is obviously no discontinuity anywhere else either, and so f(x) is continuous.

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Why did the vector cross the road?
It wanted to be normal.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: continuous

f(x) is continuous at a point a if and only if the following conditions hold:
(i) F(x) is defined at x = a
(ii) F(x) → f(a) as x → a (both from the left and from the right)

Check that your function satisfies the two conditions above.

Dragonshade

Member

Registered: 2008-01-16

Posts: 147

Re: continuous

oh yea, my bad,sorry left limit = right limit...