Question

The following is true: If f is a polynomial, then f is continuous. Which of the...

The following is true: If f is a polynomial, then f is continuous. Which of the following is also true?

a. If f is not continuous, then it is not a polynomial.

b. If f is continuous, then it is a polynomial.

c. If f is not a polynomial, then it is not continuous.

Homework Answers

Answer #1

I am attaching the pictures of solution. If you find my answer helpful please press thumbs up button. Thanks

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
For each polynomial f(x) ∈ Z[x], let f ' (x) denote its derivative, which is also...
For each polynomial f(x) ∈ Z[x], let f ' (x) denote its derivative, which is also a polynomial in Z[x]. Let R be the following subset of Z[x]: R = {f(x) ∈ Z[x] | f ' (0) = 0}. (a) Prove that R is a subring of Z[x]. (b) Prove that R is not an ideal of Z[x].
Theorem 4 states “If f is differentiable at a, then f is continuous at a.” Is...
Theorem 4 states “If f is differentiable at a, then f is continuous at a.” Is the converse also true? Specifically, is the statement “If f is continuous at a, then f is differentiable at a” also true? Defend your reasoning and/or provide an example or counterexample (Hint: Can you find a graphical depiction in the text that shows a continuous function at a point that is not differentiable at that point?)
Explain why the following statements are true or false. a) If f(x) is continuous at x...
Explain why the following statements are true or false. a) If f(x) is continuous at x = a, then lim x → a f ( x ) must exist. b) If lim x → a f ( x ) exists, then f(x) must be continuous at x = a. c) If lim x → ∞ f ( x ) = ∞ and lim x → ∞ g ( x ) = ∞ , then lim x → ∞ [ f...
#42 Which of the following statements is true? a. A continuous compounded rate of return is...
#42 Which of the following statements is true? a. A continuous compounded rate of return is higher than any discretely compounded rate of return. b. A continuous compounded rate of return is lower than any discretely compounded rate of return. c. A continuous compounded rate of return is the same as that of the discretely compounded rate of return.
Which of the following is always true for all probability density functions of continuous random variables?...
Which of the following is always true for all probability density functions of continuous random variables? A. They have the same height B. They are bell-shaped C. They are symmetrical D. The area under the curve is 1.0 Like the normal distribution, the exponential density function f(x) A. is bell-shaped B. approaches zero as x approaches infinity C. approaches infinity as x approaches zero D. is symmetrical
True or False, explain: 1. Any polynomial f in Q[x] with deg(f)=3 and no roots in...
True or False, explain: 1. Any polynomial f in Q[x] with deg(f)=3 and no roots in Q is irreducible. 2. Any polynomial f in Q[x] with deg(f)-4 and no roots in Q is irreducible. 3. Zx40 is isomorphic to Zx5 x Zx8 4. If G is a finite group and H<G, then [G:H] = |G||H| 5. If [G:H]=2, then H is normal in G. 6. If G is a finite group and G<S28, then there is a subgroup of G...
Which of the following statements is not true about continuous probability distributions? Select one: a. The...
Which of the following statements is not true about continuous probability distributions? Select one: a. The probability of any event is the area under the density curve over the range of values that make up the event. b. The total area under the density curve must be exactly 1. c. If X is a continuous random variable taking values between 0 and 500, then P(X > 200) = P(X ? 200). d. There are no disjoint events in continuous probability...
If f is continuous on ( a , b ) and f ( x ) ≠...
If f is continuous on ( a , b ) and f ( x ) ≠ 0 for all x in ( a , b ), then either f ( x ) > ______ for all x in ( a , b ) or f ( x ) < _________ for all x in ( a , b ). A function f is said to be continuous on the _______ at x = c if lim x → c +...
Which of the following statements about continuous random variables and continuous probability distributions is/are TRUE? I....
Which of the following statements about continuous random variables and continuous probability distributions is/are TRUE? I. The probability that a continuous random variable takes a specific value is 0. II. The probability that a continuous random variable takes a negative value is 0. III. The probability that any uniformly distributed random variable takes a value less than its mean is 0.5. IV. The probability that a normally distributed random variable takes a value less than its mean is 0.5.
A function f is said to be continuous on the _______ at x = c if...
A function f is said to be continuous on the _______ at x = c if lim x → c + f ( x ) = f ( c ). A function f is said to be continuous on the _______ at x = c if lim x → c − f ( x ) = f ( c ). A real number x is a _______ number for a function f if f is discontinuous at x or f...