Prove algebraically what type of function this is (even, odd, or neither).

Prove Algebraically What Type Of Function This Is (even, Odd, Or Neither).

Answers

Answer 1

The given function is even.

Solution:

If f(-x) = f(x), then the function is even.

If f(-x) = -f(x), then the function is odd.

Given function:

[tex]f(x)=x^{6}-x^{4}[/tex]

Substitute x = -x

[tex]f(-x)=(-x)^{6}-(-x)^{4}[/tex]

          [tex]=x^{6}-x^{4}[/tex]

          = f(x)   (given)

   f(-x) = f(x)

From the definition, it is even.

Hence the given function is even.


Related Questions

Given f(x) and g(x) = k·f(x), use the graph to determine the value of k.
g(x)

Answers

Explanation:

The diagram for this exercise is attached below. We have two linear functions [tex]f(x) \ and \ g(x)[/tex] and the following relationship:

[tex]g(x) = kf(x)[/tex]

From the graph, we know that:

[tex]f(-3)=1 \\ \\ g(-3)=-3[/tex]

Then, substituting into the relationship:

[tex]g(-3)=kf(-3) \\ \\ -3=k(1) \\ \\ \\ Finally: \\ \\ \boxed{k=-3}[/tex]

Other Questions
two pulleys one with adius 2 inches and the other with radius 8 inches are connected by a belt. If the 2 inch pulley is caused to rotate at 3 revolutions per minuite detirmine te revolutions per minute of the 8 inch pulley Given f(x) and g(x) = kf(x), use the graph to determine the value of k.g(x) How much HCl is produced from the reaction of an excess of HSbCl4 with 3 moles H2S in the following reaction? HSbCl4 + H2S Sb2S3 + HCl (Remember to balance the equation.) 11. Read the sentence from the passage."While he was anchored to the bench, his mind could travel anywhere."Which word from the sentence best reflects the general tone of how Mason feels about his situation?A. anchoredB. benchc. mindD. anywhere Below is a drawing of a wall that is to be covered with either wallpaper or paint. The wall is 8 ft. high and16 ft wide. The window, mirror, and fireplace are not to be painted or papered. The window measures 18 in wideand 14t. high. The fireplace is sit wide and 3 it. High while the mirror above the fireplace is 4 ft. wide and 2 ft.high. Note: this drawing is not to scale)How many square feet of wallpaper are needed to cover the wall? Sin(pi/2-x)/cot^2(pi/2-x)+1 Assume that an economy described by the Solow model is in a steady state with output and capital growing at 3 percent, and labor growing at 1 percent. The capital share is 0.3. The growth-accounting equation indicates that the contributions to growth of capital, labor, and total factor productivity are:____________-A) 0.3 percent, 0.7 percent, and 2 percent, respectively.B) 0.9 percent, 0.7 percent, and 1.4 percent, respectively.C) 0 percent, 1 percent, and 2 percent, respectively.D) 1.8 percent, 0.3 percent, and 0.9 percent, respectively. How could this gravitational potential energy be transformed into kinetic energy? A. He could start the engine. B. He could release the brakes. C. He could push it up the hill. D. all of these A speaker whose sentences were very similar to those used in a news article would be _____, if he or she did not acknowledge that the phrasing came from the article. ____________________ and _______________ encompass the largest amount of noncompliant establishments, who fall in the least demanding category of compliance. 1) Write in the formula. What equals the perimeter P of the rectangle wich is 25 cm wide. (show the length with the letter b.) 2) Calculate the perimeter of the rectangle when its length is equal to:a) 45 cm; b) 0.25 m; c) 650 mm; d) 3 m by 9 cm; e) 3 dm.Please I really need help Why does math get so hard that you have an answer but you forget what your answer was because it was so so so so so so so so so so so so so so hard.Why is it hard? On her first visit to China, Jane did not know how to pay for the produce she had selected at a market. She watched several Chinese women pay for their selections, and then Jane copied their behavior. In this example, Jane used ________. If the average mass of an adult is 86kg. Determine the mass and weight of an 86kg man in the moon where gravitational field is one-sixth that of the earth. One of the Ten Principles of Economics in Chapter 1 is that people face tradeoffs. The growth that arises from capital accumulation is not a free lunch. It requires that societyA.conserve resources for future generations.B.sacrifice consumption goods and services now in order to enjoy more consumption in the future.C.recycle resources so that future generations can produce goods and services with the accumulated capital.D.None of the above is correct. In a survey of 5100 randomly selected T.V. viewers, 40% said they watch network news programs. Find the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V. viewers who watch network news programs. Information processing guided by higher-level mental processes is called Martha claims that she has been assigned marginal job roles or light workloads that don't lead to promotion. Which of the following terms accurately explains the type of discrimination she has been subjected to?A) intimidationB) sexual harassmentC) exclusionD) inclusionE) insult Which of the following is the least likely strategy for a U.S. firm that will be purchasing Swiss francs in the future and desires to avoid exchange rate risk (assume the firm has no offsetting position in francs)? a. Purchase a call option on francs. b. Sell a futures contract on francs. c. Obtain a forward contract to purchase francs forward. d. All of the above are appropriate strategies for the scenario described. Identify the factors that led to rise of early empires and states in the centuries after 1200, and describe the main characteristics of each. What was the nature of the connection between empires and war. Religion and trade? Have those connections changed much at all for modern empires? Explain. Steam Workshop Downloader