# Discuss continuity of the composite function

1. Feb 27, 2009

### louie3006

1. The problem statement, all variables and given/known data :
discuss continuity of the composite function h(x)=f(g(x)) when A} F(x)=X^2 , g(x) = x-1
B} f(x) = 1/x-6 , g(x) = X^2+5
where should I start ?

2. Feb 27, 2009

### snipez90

Re: continuity

h is continuous at a point a if f is continuous at g(a)

3. Feb 27, 2009

### louie3006

Re: continuity

and how can we find out what a is if we are not given a number for a ?

4. Feb 27, 2009

### HallsofIvy

Staff Emeritus
Re: continuity

Consider all numbers! At what values of x is f(x)= 1/(x- 6) NOT continuous? (That's the crucial question.)

5. Feb 27, 2009

### louie3006

Re: continuity

when x = -6, that would make f(x) = 1/x-6 discontinuous right?

6. Feb 27, 2009

### HallsofIvy

Staff Emeritus
Re: continuity

Please use parentheses.
If you mean f(x)= (1/x)- 6, then f(-6)= -1/6- 6= -37/6. No this function is not discontinuous at -6.

If you mean f(x)= 1/(x- 6), then f(-6)= 1/(-6-6)= -1/12. No this function is not discontinuous at -6.

Be more careful!

7. Feb 27, 2009

### louie3006

Re: continuity

f(6) = 1/ (6-6) = 1/0 this function is discontinuous, right ?

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook