if a function f is defined such that f(x+3) = f (x) + f(3) show that f(-3) = -f(3)

Answers

Answer 1

Answer:

[tex]Solution,\\f(x+3)=f(x)+f(3).......(1)\\Put~x=0~in~eq^n~(1),\\f(0+3)=f(0)+f(3)\\or, f(3)=f(0)+f(3)\\or, f(0)=0.........(2)\\Now,\\Put~x=-3~in~eq^n(1),\\f(-3+3)=f(-3)+f(3)\\or, f(0)=f(-3)+f(3)\\From~eq^n(2),\\0 = f(-3)+f(3)\\or, f(-3)=-f(3)~proved[/tex]


Related Questions

A bakery sold 73 bagels in the first hour of business. If the bakery had 246 bagels to start with, how many bagels were left after the first hour?

Answers

Answer:

173

Step-by-step explanation:

Answer:  173 bagels are left after the first hour.

Step-by-step explanation:  if they had 246 bagels to start with, and they sold 73 in the first hour. 246-73=173.

On in-line skates, Bradley skates 4 miles in 48 minutes. At this speed, how long would it take him to skate the entire length of a 12-mile bike path?

Answers

Answer:

144 minutes

Step-by-step explanation:

4 goes in 12 3 times so we have to do 48 times 3 too. Which is 144.

Answer:

Step-by-step explanation:

[tex]\frac{t}{12}=\frac{48}{4}\\ \\ t=144min[/tex]

How do I find the density? Harold is a woodworker and is interested in finding the density of two different types of wood. He bought a pine log that has a 5-inch radius and is 30 inches long. The weight of the log is approximately 42.63 pounds.

Answers

Answer:

The density of the pine log is 0.2842 pounds per inch.

Step-by-step explanation:

To calculate the density of an object, you must divide its mass by its volume (radius times height). Thus, given that the pine log that has a 5-inch radius and is 30 inches long, while its weight is approximately 42.63 pounds, the following calculation must be performed to determine its density:

X = 42.63 / (30 x 5)

X = 42.63 / 150

X = 0.2842

Thus, the density of the pine log is 0.2842 pounds per inch.

Omari types 300 words in 6 minutes. How many words does he type in 2 minutes?
In 1 minute?

Answers

Answer:

50 words per minute.

100 words per 2 minutes.

Step-by-step explanation:

Hope this helps!

What’s the probability tree?

Answers

Answer:

The first event is represented by a dot. From the dot, branches are drawn to represent all possible outcomes of the event. The probability of each outcome is written on its branch.

Step-by-step explanation:

As Venus revolves around the sun, it travels at
rate of approximately 22 miles per second. Convert this rate to kilometers
per second. At this rate, how many kilometers will Venus travel in 20 seconds? In your computations, assume that 1 mile is
equal to 1.6 kilometers. Do not round your answers.

Answers

22 x 1.6= 35.2km per second

35.2 x 20 = 704km in 20 seconds

HELP ASAP PLEASE!
An airplane cuts through the morning sky. For every 1,000 feet that it climbs, the outside temperature drops 20 degrees Fahrenheit. What is the rate of temperature change in degrees Fahrenheit per foot? Complete the steps below to answer the question.

part A: Write the change in elevation and the change in temperature as rational numbers.

part B: Write a numerical expression to represent the rate of temperature change in degrees Fahrenheit per foot.

part C: What is the rate of temperature change in degrees Fahrenheit per foot?

part D: Now, consider the reverse situation: as the airplane descends, or drops, 1,000 feet in the air, the temperature rises 20 degrees Fahrenheit. Write a numerical expression representing the rate of temperature change in degrees Fahrenheit per foot.

part E: What is the rate of temperature change in degrees Fahrenheit per foot?

part F: How is the rate you found in part E related to the rate you found in part C? What does this mean?

Please answer each question separately! :(​

Answers

Step-by-step explanation:

The air plane is rising so the change in elevation is +1000 feet. The temp dropped and is -20 degrees fahrenheit.

1 degree per 50 ft

For every 1,000 feet that it climbs, the outside temperature drops 20 ... What is the rate of temperature change in degrees Fahrenheit per foot.

Hope I helped

Answer:

Step-by-step explanation:

part A=The airplane is rising, so the change in elevation is +1,000 feet. The temperature is dropping, so the change in temperature is -20 degrees Fahrenheit.

Part B= -20 degrees fehrenheit/1,000 feet

Part C=  -20 degrees fehrenheit/1,000 feet= -1 degrees fehrenheit/50 feet

The answer can also be written as -1 degrees fehrenheit/50  per foot.

Part D = The airplane is descending, so the change in elevation is -1,000 feet. The temperature is rising, so the change in temperature is +20 degrees Fahrenheit.

The rate of temperature change in degrees Fahrenheit per foot is 20/-1000

Part E= The answer can also be written as-1/-50

Part F= The rate in part E is equal to the rate in part C. It means that -1/50=1/-50=-1/-50

please please mark as brainliest.!!!

Which rational number is less than 4/9​

Answers

Answer:

Step-by-step explanation:

The number 4/9 is a rational number. It is a ratio, or fraction, made up of two integers, 4 and 9. So a rational number less than 4/9 will be any fraction less.

ABDC is a kite . AB =AC and DB=DC , Angle A = 80 degree and angle D=62 degree . find angles B and C​

Answers

Step-by-step explanation:

you have quand app download and photo this one and come answer

your questions photo and come answer

Help would be much appreciated ​

Answers

X = 68 is your answer hope this helps!

Each circle counts as one whole. Write a mixed number giving the amount shaded. Then, write this amount as an improper fraction.​

Answers

itis 8 cause we added

I only need the answer FAST​

Answers

Cars:        1             2              3

Trucks:    4             8             12

1 : 4 = 2 : x

4 · 2 = 1 · x

8 = x

1 : 4 = x : 12

4 · x = 1 · 12

4x = 12

x = 12 ÷ 4

x = 3

(11 - 3) x [ 15 + (10 - 5)] write 3 steps using pemdas

Answers

Answer:

160

Step-by-step explanation:

What is the value of y?

Answers

I think it’s b but I’m not sure
B is the answer
please give me points

Can someone help me, please??

Answers

Answer:

im gonna say its the last one

Step-by-step explanation:

all of the graphs and histograms ive seen have a 0 at the y

I have an idea. We all know that Gen z is way too powerful at this point so let's turn this into Twitter for students. answer yes if you with me. also, make this blowup

Answers

yea sure lets go lolol

If R, S, and T are collinear and RS + ST = RT, which of the following is true?

T is between R and S.
RS = RT
S is between R and T.
S is the midpoint of ./rt

Answers

Answer:

[tex]S \: is \: between \: R \: and \: T.[/tex]

Answer:

S is between R and T.

Step-by-step explanation:

5. Ms. Gallegos burns 236 calories riding her bike each hour. She wants to burn more
than 590 calories riding her bike at the same rate.
Which inequality represents all possible values for t, the number of hours Ms. Gallegos
must ride her bike to burn more than 590 calories? 6.10A
A. t > 2.5
B. t < 2.5
C. t > 0.4
D. t < 0.4

Answers

Answer:

c

Step-by-stepc explanation:

Solve for y
4y + 5x = 8.
O y = -5x + 8
O 4y = -5x + 8
O y = 5/4x + 2
O y = -5/4x + 2

Answers

Answer:

y= -5/4x+2

Step-by-step explanation:

probably wrong but it definitely is one of the bottom two answers

Answer:

yes is D. bk$kdknxnxnxncncncncncj

Shannon and her family are traveling in the car. Her mom brought 1/2 pound of raisins to share equally between the four
family members. How much will each person get?

Answers

Answer:

1/8 pound per person

Step-by-step explanation:

Please help me out tysm

Answers

Answer: 1/4 s^2 or [tex]\frac{1}{4} s^{2}[/tex]

convert 131 57’ 32” to decimal degree

Answers

Answer:

131.95888888888888

Step-by-step explanation:

Your Welcome :)

111=14g What the answer

Answers

Answer:

[tex]g = \frac{111}{14} [/tex]

Step-by-step explanation:

[tex]111 = 14g[/tex]

[tex]14g = 111[/tex]

[tex]g = \frac{111}{14} [/tex]

Insta: 25k_kem

me encontré $100, luego mi papá medio $80, pero yo le di a mi mamá $70 cuánto me queda​

Answers

Answer:

te queda $110

Step-by-step explanation:

espero que te sirva

Convert x + 3y = 9 into slope-intercept form

Answers

Answer:

3y=-x+9

y=1/3x+3

Step-by-step explanation:

9 bags with 342 cans. what is the rate of cans per bag? _ cans per bag​

Answers

Answer:

(-2) + (3-7)

(-1) * (-2)

EVALUATE THE EXPRESSION

Step-by-step explanation:

HELP ME ON THIS QUESTION PLSZSZS

~!!!! HELP ME PLEASE IM IN 7TH GRADE AND LEARNING 9TH AND 8TH iM SUFFERING !!!!~
QUESTION~
Find the vertex of the graph of
f(x) = −|0.75x + 1.5|. Tell whether the
graph opens upward or downward.

Answers

this is what it looks like when I graphed it.

Asher is pet sitting for five dogs. He only has of a bag of dog food left for the day. If each dog gets the same amount, what fraction of the bag will each dog get?

Answers

Answer:

1/5

Step-by-step explanation:

u split evenly between five dogs so they will each get 1/5 of the bag

Pls help I’ll brainlest ASAP pls

Answers

Answer:

p=4

Step-by-step explanation:

Which of the following is a composite number between 1 and 10? A. 5 B. 3 C. 7 D. 4

Answers

Answer:

b

Step-by-step explanation:

Answer:

Answer is D.

Step-by-step explanation:

I hope it's helpful!

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