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c.F(x) is a complace of features that are continuous for all real numbers, so it is constant at eextremely number in its domajor.

You are watching: Explain, using the theorems, why the function is continuous at every number in its domain.

Step 1:

The feature

.

Since the degree of the numerator and also the denominator of the function is exact same, the function

is a imcorrect polynomial feature.

Domain:

The doprimary of a role is for all values of x, which renders the function mathematically correct.

Due to the fact that there shouldn"t be any zero in denominator.

The denominator expression

is constantly better than one.

,for all values of x.

So the doprimary of any type of polynomial attribute

.

Any polynomial attribute is consistent on its doprimary.

Hence the attribute

is constant at eextremely number on
.

is a rational feature, so it is continuous at eincredibly number in its domain.

Solution:

Option (b) is correct choice.

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is a rational attribute, so it is constant at eexceptionally number in its doprimary.