1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tanya [424]
3 years ago
15

Suppose f is a continuous function on [-2, 2) such that

Mathematics
1 answer:
Leviafan [203]3 years ago
4 0

Answer:

2. a and b only.

Step-by-step explanation:

We can check all of the given conditions to see which is true and which false.

a. f(c)=0 for some c in (-2,2).

According to the intermediate value theorem this must be true, since the extreme values of the function are f(-2)=1 and f(2)=-1, so according to the theorem, there must be one x-value for which f(x)=0 (middle value between the extreme values) if the function is continuous.

b. the graph of f(-x)+x crosses the x-axis on (-2,2)

Let's test this condition, we will substitute x for the given values on the interval so we get:

f(-(-2))+(-2)

f(2)-2

-1-1=-3  lower limit

f(-2)+2

1+2=3 higher limit

according to these results, the graph must cross the x-axis at some point so the graph can move from f(x)=-3 to f(x)=3, so this must be true.

c. f(c)<1 for all c in (-2,2)

even though this might be true for some x-values of of the interval, there are some other points where this might not be the case. You can find one of those situations when finding f(-2)=1, which is a positive value of f(c), so this must be false.

The final answer is then 2. a and b only.

You might be interested in
Three consecutive even numbers have a sum where one half of that sum is between 90 and 105.
dexar [7]
n;\ n+2;\ n+4-three\ consecutive\ even\ numbers\\\\90 \ \textless \  \dfrac{1}{2}(n+n+2+n+4) \ \textless \  105\\\\90 \ \textless \  \dfrac{1}{2}(3n+6) \ \textless \  105\ \ \ |multiply\ both\ sides\ by\ 2\\\\180 \ \textless \  3n+6 \ \textless \  210\ \ \ |subtract\ 6\ from\ both\ sides\\\\174 \ \textless \  3n \ \textless \  204\ \ \ |divide\ both\ sides\ by\ 3\\\\58 \ \textless \  n \ \textless \  68\\\\Answer:\\60;\ 62;\ 64\ or\ 62;\ 64;\ 66;\ or\ 64;\ 66;\ 68\ or\ 66;\ 68;\ 70.
5 0
2 years ago
Read 2 more answers
Which statements describes the function f(x)=2(x-4)^4
kap26 [50]
You're right, c is the answer because the function is a parabola because of the power of four
6 0
3 years ago
Read 2 more answers
Which type of programmer designs programs for applications executed on the internet
Artyom0805 [142]
Regardless of what anyone says, there really isn't an official name for us I guess "Web Developer" or "Web Designer."
6 0
3 years ago
Forest Gump ran for 13 hours and went 65 miles. What is the unit rate (how many miles did he run per hour)?? Explain your answer
Leni [432]
Okurr I’m just responding so I can answer a question but idk anything so I’m just typing to finish setting up my account..❤️
3 0
3 years ago
In this parallelogram m angle bad =75 so m angle bcd
Allisa [31]
The complete question in the attached figure

we know that
m angle bad =75°
remember that on parallelogram 
(∠A + ∠<span>B) = 180°
[Since, sum of the interior angles on the same side of the transversal is 180°] 
therefore
</span>∠B=180°-∠A=180°-75°=105°
∠B=105°
<span>Similarly
∠B + ∠C = 180°
∠C + ∠D = 180°
and ∠D + ∠A = 180°</span>
<span>Thus, the sum of any two adjacent angles of a parallelogram is 180°.
</span>
m angle bcd=∠C=180-∠B=180°-105°=75°

the answer is m angle bcd=75°

8 0
3 years ago
Other questions:
  • Write this number in word form 45,920
    8·2 answers
  • What is the sum of 8 and 7 doubled in a numerical expression
    8·1 answer
  • Please Help!! I will give brainliest to the quick and correct answer
    11·1 answer
  • (PLEASE HELPPP!!!)
    12·1 answer
  • What is the value of the expression
    6·1 answer
  • Can someone please help me
    14·1 answer
  • Please help me with this! I will appreciate the help :)
    5·1 answer
  • Help me pleaseeee already due!!
    12·1 answer
  • If f(x) = 2x - 4 and g(x)= -5x + 6, then what is f(g(x))?
    12·1 answer
  • What is the midline equation for the function h(x)=−3cos(πx+2)−6?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!