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My function doubts!

  • \(If\quad f\left( x+3 \right) \quad =\quad { x }^{ 2 }+x-6,\quad then\quad find\quad f(x).\quad\)

  • \(If\quad f(x+3)\quad =\quad { x }^{ 2 }-7x+2,\quad find\quad the\quad remainder\quad when\quad f(x)\quad is\quad divided\quad by\quad x+1.\)

Please help me with the problems, Thanks!

Note by Swapnil Das
2 years, 6 months ago

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They are very easy.

1.\(\text{Let g(x) = f(x), Not let y = x+3, we get} \\ g(y) = (y-3)^2 + (y-3) - 6 \\ f(x) = x^2 - 5x\)

2.\(\text{We know that the remainder will be f(-1). We have to find f(-1) } \\ \text{We know that } f(x+3) = x^2 -7x +2 \\ \text{Now if we let x = -4 we'll get f(-1) hence our answer.} \\ \text{Hence f(-1) will be} f(-1) = (-4)^2 - 7(4) + 2 = 46 \)

Rajdeep Dhingra - 2 years, 6 months ago

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@Swapnil Das @Sravanth Chebrolu I think you must revise the simple remainder- theorem for the 2nd question.

Nihar Mahajan - 2 years, 6 months ago

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Yup, I have. I just got a last doubt in the chapter, so I asked for help. Well I was now solving problems of Newton's Sums. @Nihar Mahajan

Swapnil Das - 2 years, 6 months ago

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let, x+3 =y......

make a new function.....

and solve....

Parth Tandon - 2 years, 6 months ago

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i think i am little slow in typing.......:p

Parth Tandon - 2 years, 6 months ago

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Why do you think so?

Sravanth Chebrolu - 2 years, 6 months ago

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@Sravanth Chebrolu when i started posting the solution there were no comments but as soon as i finished i found 6 comments hovering around....:)

Parth Tandon - 2 years, 6 months ago

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@Parth Tandon Whoah! That happens to me too! But, don't consider that as your inability.

Sravanth Chebrolu - 2 years, 6 months ago

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@Sravanth Chebrolu ya.........

i am working on it......

always used to work with a pen and paper so..................

Parth Tandon - 2 years, 6 months ago

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@Parth Tandon Oh yes! The classic method of pen and paper . . . :P

Sravanth Chebrolu - 2 years, 6 months ago

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can someone tell me what is multi_step decryption.....?

Parth Tandon - 2 years, 6 months ago

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  • First question: the answer is \(x^{2}-5x\)

  • Second question: the answer is \(46\).

Am I right? If I am I'll post the solution. Please reply @Swapnil Das

Sravanth Chebrolu - 2 years, 6 months ago

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Ur answer to 2nd one is wrong. For a level 5 like U it should Child's play. Anyways u can see my solution. Cheers!

Rajdeep Dhingra - 2 years, 6 months ago

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Sorry, I got it wrong as I got meddled up with the signs, I posted it correctly on Swapnil's message board though, cheers! xD

Sravanth Chebrolu - 2 years, 6 months ago

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@Sravanth Chebrolu Yeah!

Swapnil Das - 2 years, 6 months ago

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@Swapnil Das Hey! I posted a question on logic just now, as you wanted me to post such questions I did it, here's the link!

Sravanth Chebrolu - 2 years, 6 months ago

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@Sravanth Chebrolu See who have solved...

Swapnil Das - 2 years, 6 months ago

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@Swapnil Das Omg! That was qiuck! Hope you liked it. . .

Sravanth Chebrolu - 2 years, 6 months ago

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Hey Sravanth, I don't know how I am getting some other remainder. Can you post the 2nd solution please?

Swapnil Das - 2 years, 6 months ago

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Sure. Here it is.

As you know how to make expression, you'll get \(f(x):x^2-13x-10\)

Dividing it by \(x+1\), we get \(4\). . .

Sravanth Chebrolu - 2 years, 6 months ago

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Can you please tell me how it became -5y instead of -5x?

Swapnil Das - 2 years, 6 months ago

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BTW, I liked the new look of Brilliant! But I didn't find the explore icon anywhere. . .

Sravanth Chebrolu - 2 years, 6 months ago

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@Sravanth Chebrolu community.............

Parth Tandon - 2 years, 6 months ago

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@Parth Tandon Not the community, the was an icon explore, I didn't find that...

Sravanth Chebrolu - 2 years, 6 months ago

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@Sravanth Chebrolu u can check community ....................

i think explore renamed to community................

latest posts are there which before were given under explore................

Parth Tandon - 2 years, 6 months ago

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@Parth Tandon Yes. I saw that. Thank you very much!

Sravanth Chebrolu - 2 years, 6 months ago

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@Sravanth Chebrolu welcome...............

do u know what is multi step decryption or i hv to search on net.....?

Parth Tandon - 2 years, 6 months ago

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@Parth Tandon I did hear about that in a novel Digital Fortress, but I don't know much about it. . . :(

Sravanth Chebrolu - 2 years, 6 months ago

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@Sravanth Chebrolu ok then........................

thnx for giving a thought to it..................

Parth Tandon - 2 years, 6 months ago

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@Parth Tandon Welcome!

Sravanth Chebrolu - 2 years, 6 months ago

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@Parth Tandon multi step decryption...............?

Parth Tandon - 2 years, 6 months ago

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@Sravanth Chebrolu May I help U?

Swapnil Das - 2 years, 6 months ago

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@Swapnil Das anyone.....?

multi step decryption....?

Parth Tandon - 2 years, 6 months ago

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Sorry, that was a typo there! It's edited now.

Sravanth Chebrolu - 2 years, 6 months ago

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I think you are right. Please post the solution.

Swapnil Das - 2 years, 6 months ago

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But I think it's already posted! :P

Sravanth Chebrolu - 2 years, 6 months ago

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@Sravanth Chebrolu Well Rajdeep also did the same, BTW thank you very much. Just a request, if you have time anytime, please post problems of this format, I would surely like them!

Swapnil Das - 2 years, 6 months ago

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@Swapnil Das

We'll take that into consideration. :P

Surely! I'll keep posting suchquestions!

Sravanth Chebrolu - 2 years, 6 months ago

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@Sravanth Chebrolu Go to Community-All topics-Problems

Swapnil Das - 2 years, 6 months ago

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@Swapnil Das Okay. So that's nothing but explore?

Sravanth Chebrolu - 2 years, 6 months ago

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@Sravanth Chebrolu yeah!

Swapnil Das - 2 years, 6 months ago

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@Swapnil Das Thank you very much! BTW, how did you like the new look?

Sravanth Chebrolu - 2 years, 6 months ago

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@Sravanth Chebrolu Nice!

Swapnil Das - 2 years, 6 months ago

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