Discuss continuity of the composite function

[louie3006]

Homework Statement

:
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 ?

 

[snipez90]

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

 

[louie3006]

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

 

[HallsofIvy]

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

 

[louie3006]

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

 

[HallsofIvy]

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

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!

 

[louie3006]

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