Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,459 questions

17,854 answers

1,446 comments

811,086 users

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

0 votes

 

F(x) = 
2x2  x  8
x2 + 1
 
a.F(x) is a polynomial, so it is continuous at every number in its domain.
b.F(x) is a rational function, so it is continuous at every number in its domain.
c.F(x) is a composition of functions that are continuous for all real numbers, so it is continuous at every number in its domain.
d.F(x) is not continuous at every number in its domain.
e.none of these

State the domain. (Enter your answer using interval notation.)

asked Feb 1, 2015 in CALCULUS by anonymous

1 Answer

0 votes

Step 1:

The function .

Since the degree of the numerator and the denominator of the function is same, the function is a improper polynomial function.

Domain:

The domain of a function is for all values of x, which makes the function mathematically correct.

Since there shouldn't be any zero in denominator.

The denominator expression is always greater than one.

,for all  values of x.

So the domain of any polynomial function  .

Any polynomial function is continuous on its domain.

Thus the function is continuous at every number on  .

is a rational function, so it is continuous at every number in its domain.

Solution:

Option (b) is correct choice.

is a rational function, so it is continuous at every number in its domain.

answered Feb 2, 2015 by yamin_math Mentor

Related questions

...