Let f
f
be the function given by f(x)=∣∣x2−3∣∣⋅(x+0.5)(x2−3)(x+0.5)< br /> f
(
x
)
=
|
x
2
−
3
|
⋅
(
x
+
0.5
)
(
x
2
−
3
)
(
x
+
0.5
)
. on which of the following open intervals is f
f
continuous?

The function is continuous on all subsets of real numbers.

Explanation:

The function f(x)=∣x^2−3∣*(x+0.5)*(x^2−3)*(x+0.5) is composed by the multiplication of 4 parts. The first one, ∣x^2−3∣, is continuous for all real numbers because is composed by h(g(x)) = |g(x)| and  g(x) = x^2−3 where both are continuous for all real numbers. The other 3 parts are the polynomials  (x+0.5), (x^2−3) and (x+0.5); all polynomials is continuous for all real numbers. So, f(x), the multiplication of these continuous functions, is in consequence continuous on all subsets of real numbers.

the answer is c.

by: nicholas dooley

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