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Similar to menentukan fungsi komposisi dan fungsi invers
Similar to menentukan fungsi komposisi dan fungsi invers (20)
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menentukan fungsi komposisi dan fungsi invers
- 1. Fungsi Operasi Fungsi, Komposisi Fungsi dan Invers Ratna Wijayanti,M.Pd. ratnawijayanti@uym.ac.id
- 2. Operasi Fungsi 𝑓 + 𝑔 𝑥 = 𝑓 𝑥 + 𝑔 𝑥 𝑓 − 𝑔 𝑥 = 𝑓 𝑥 − 𝑔 𝑥 𝑓. 𝑔 𝑥 = 𝑓 𝑥 . 𝑔 𝑥 𝑓 𝑔 𝑥 = 𝑓(𝑥) 𝑔(𝑥) Jika diketahui fungsi 𝑓 dan 𝑔, kita dapat membuat fungsi baru dgn melakukan operasi penjumlahan, pengurangan, perkalian, pembagian. Catatan: a. Jika D(f+g)=D(f)∩D(g) b. Jika D(af)=D(f) c. Jika D(fg)=D(f)∩D(g) dan, d. Jika D(fg)(x)=D(f)∩D(g),g(x)≠0
- 3. Komposisi Fungsi Jika 𝑓 bekerja pada 𝑥 menghasilkan 𝑓 (𝑥) dan 𝑔 bekerja pada 𝑓 (𝑥) menghasilkan 𝑔 (𝑓 (𝑥)) , dikatakan kita telah menyusun 𝑔 dgn 𝑓. Fungsi yg dihasilkan disebut KOMPOSISI 𝑔 dgn 𝑓, dinyatakan dgn 𝑔 ∘ 𝑓.
- 4. Fungsi Invers Jika 𝑓 bekerja pada 𝑥 menghasilkan 𝑓 (𝑥) dan 𝑔 bekerja pada 𝑓 (𝑥) menghasilkan 𝑔 (𝑓 (𝑥)) , dikatakan kita telah menyusun 𝑔 dgn 𝑓. Fungsi yg dihasilkan disebut KOMPOSISI 𝑔 dgn 𝑓, dinyatakan dgn 𝑔 ∘ 𝑓.
- 5. The essence of calculus Mercury takes a little more than 58 days to complete its rotation, so try to imagine how long days must be there! Since the temperatures are so extreme, albeit not as extreme as on Venus, Mercury has been deemed to be non-habitable for humans Mercury is the closest planet to the Sun and the smallest one in the entire Solar System. Contrary to popular belief, this planet's name has nothing to do with the liquid metal. Mercury was, instead, named after the famous Roman messenger god Mercurius
- 6. Mathematical tapestry Do you know what helps you make your point crystal clear? Lists like this one: ● They’re simple ● You can organize your ideas clearly ● You’ll never forget to buy milk! And the most important thing: the audience won’t miss the point of your presentation
- 7. Calculus demystified Venus has a beautiful name and is the second planet from the Sun. It’s hot and has a poisonous atmosphere Mercury is the closest planet to the Sun and the smallest one in the Solar System—it’s only a bit larger than the Moon Mercury Venus
- 8. The calculus code Mercury is the closest planet to the Sun and the smallest of them all Venus has a beautiful name and is the second planet from the Sun Despite being red, Mars is actually a cold place. It’s full of iron oxide dust Mercury Venus Mars
- 9. Mastering the calculus frontier Mars is actually a very cold place Venus has extremely high temperatures Jupiter is the biggest planet of them all Saturn is a gas giant and has several rings Mars Jupiter Venus Saturn
- 10. Venus has extremely high temperatures Neptune is the farthest planet from the Sun The mathematical landscape Mars is actually a very cold place Mercury is the closest planet to the Sun Saturn is a gas giant and has several rings Jupiter is the biggest planet of them all Mars Venus Neptune Mercury Saturn Jupiter
- 11. Awesome words
- 12. “This is a quote, words full of wisdom that someone important said and can make the reader get inspired” —Someone Famous
- 13. A picture is worth a thousand words
- 14. The power of derivatives Images reveal large amounts of data, so remember: use an image instead of a long text. Your audience will appreciate it
- 15. 98,300,000 Big numbers catch your audience’s attention
- 16. Jupiter’s rotation period 9h 55m 23s 333,000 The Sun’s mass compared to Earth’s 386,000 km Distance between Earth and the Moon
- 17. Exploring calculus wonders Mercury is the closest planet to the Sun and the smallest of them all Mercury Venus has a beautiful name and is the second planet from the Sun Venus Despite being red, Mars is actually a cold place. It’s full of iron oxide dust Mars 50% 75% 25%
- 18. Calculus chronicles You can replace the image on the screen with your own work. Just right-click on it and select “Replace image”
- 19. Calculus unveiled You can replace the image on the screen with your own work. Just right-click on it and select “Replace image”
- 20. A calculus expedition Venus has a beautiful name and is the second planet from the Sun. It’s hot and has a poisonous atmosphere Venus
- 21. A calculus showcase STEP 1 STEP 2 20XX Mercury is the closest planet to the Sun 20XX Saturn is one of the planets that has rings 20XX Venus has a beautiful name, but it’s hot 20XX Mars is a very cold place for humans to live
- 22. Shaping mathematical thought Game Engaging Interactive Enjoyable Mars is a red planet Mercury is very small Venus is a hot planet Jupiter is a gas giant
- 23. Calculus frontiers Team A Team B Team C Team D Mercury 0.06 0.53 0.38 0.38 Mars 0.11 9.4 0.53 0.78 Saturn 95.2 1.16 9.4 1.16
- 24. Exploring mathematical elegance Follow the link in the graph to modify its data and then paste the new one here. For more info, click here Venus Planet Venus has high temperatures Saturn Saturn is a gas giant with rings
- 25. Kaliyah Harris Stephen Hill Our team You can speak a bit about this person here You can speak a bit about this person here
- 26. Rubric Element Poor Fair Strong Clear claim with reason Unclear. No reason given Claim is clear. Reasons unclear Claim and reason clearly stated Evidence No evidence provided Attempts to support the claim Supports the central with facts Explanation Contains little explanation or analysis Attempts to explain and analyze the Clearly explains and analyzes most of the
- 27. Multiple choice questions Mercury is the closest planet to the Sun and the smallest one in the Solar System—it’s only a bit larger than the Moon Mars is actually a cold place for humans Venus has extremely high temperatures Neptune is the farthest planet from the Sun ✔
- 28. Short answer questions Question Consider the function F(x)=3x-2x+5. Find the derivative f'(x) Answer The derivative of the function is 6x-2 Tip: To find the derivative f'(x), we'll apply the power rule and constant rule
- 29. The derivative f’(x)=lim f(x + dx) - f(x) dx Choose an interval Find the raw change Find the rate of change Make your model perfect 01 02 03 04
- 30. Provide solutions to these problems Practical application y'(x)=5x-3x+7 Power rule: If (x)= ax, then f'(x)= nax(n-1) y'(x)=10x-3+0 10x=3 Answer: 3 Use this espace to resolve the problem g(x)= 4x-6x+2x-1 Answer: Use this espace to resolve the problem h(x)= 2e+31n(x) Answer:
- 31. Calculus in real-world applications Write a short essay choosing one of the topic on the right. It’s important: ● Define a clear thesis statement that conveys the main point of your essay ● Create a well-structured outline to organize your ideas ● Craft an attention-grabbing introduction and a strong, concise conclusion Calculus in Engineering Mercury is the closest planet to the Sun and the smallest one Technological Advancements Venus has extremely high temperatures for humans
- 32. Power and chains Mercury is the smallest in the Solar System Derivative Despite being red, Mars is a very cold place Power rule Neptune is the farthest planet from the Sun Chain rule
- 33. Mathematical abstraction Calculus 01 02 Despite being red, Mars is a very cold place to live Despite being red, Mars is a cold place Saturn is a planet that has rings Saturn is one of the planets that has rings Jupiter is the biggest planet of them all Neptune is the farthest planet
- 34. CREDITS: This presentation template was created by Slidesgo, and includes icons by Flaticon, and infographics & images by Freepik Thanks! Do you have any questions? youremail@freepik.com +34 654 321 432 yourwebsite.com Please keep this slide for attribution