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c.F(x) is a composition of attributes that are constant for all actual numbers, so that is constant at every number in that domain.

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

Step 1:

The function

.

Since the level of the numerator and also the denominator of the function is same, the function

is a wrong polynomial function.

Domain:

The domain the a duty is for all worths of x, which provides the role mathematically correct.

Since over there shouldn"t be any kind of zero in denominator.

The denominator expression

is always greater 보다 one.

,for all values of x.

So the domain of any type of polynomial function

.

Any polynomial duty is consistent on that domain.

Thus the function

is continuous at every number on
.

is a reasonable function, so that is continuous at every number in that is domain.

Solution:

Option (b) is correct choice.

See more: In Texas, Failure To ________________ Can Cause You To Be Imprisoned For 5 Years.

is a rational function, so that is constant at every number in that domain.