# What is f(x). I've been trying to understand it for so long, but I always get different answers, I feel like I'm going crazy. Please someone explain it and read my whole question carefully.

What is f(x)? I've gotten so many different answers , let's say f(x)=x²+15x+50, now I was told before that that means we have a function called f, when we inputted x into it f squared it then added 15 times it then added 50, now that makes sense until I'm asked something like "find the zeros of this function". Because we always find the zeros using the output, which in this case after we inputted x into f we got x²+15x+50. But why do we solve in terms of the output , aren't we trying to find the input values that when inputted into the function f it will output 0. X²+15x+50 is already an output , I hope you understand what I'm trying to say. Also I'm in 12th grade I've solved hundreds upon hundreds of these types of questions I've just never tried to understand what the whole notation actually meant . Someone also told me that f(x) doesn't mean what I said above, where it means to input x into f and have it output something . He said it meant it's a function in terms of x and whatever comes after the = shows what we do to any x , that makes no sense to me. So can someone please explain #1 what f(x) and whatever comes after it means . #2 why we set the output of the function when we inputted x into it to 0 when we're finding zeros even though it's already an output. Thank you .

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The whole I came to this website was to ask people who were more knowledable than me and for them to answer me, not for them to give me an ai generated answer from chat gpt. Why would you accept the answer if you were just gonna paste in chat gpt, I could've done that .

This is not from chat gpt! Do you have any further question that I have not answered? I would be happy to clear them out.

It obviously is, it's the exact same format and wording that chat gpt uses.

Do you have any questions that I did not answer in my response? I would be happy to answer them.

You didn't answer the whole first part of the question. I never said that my understanding of a function is that for any value of x you input in f, the output will be calculated using the formula x²+15x+50. I said that my understanding was that when we input x into f, f squares x then multiples it by 15 then adds 50. I was asking if this is correct then why do we use the output of x as a means to find the zeros.

I will revise my answer and make this clear for you shortly.

I added extra details. Let me know if you have any further questions.

The first part of the question is the more important part and you keep ignoring it, I know how to get zeros that was never my question it feels like I'm going in circles. I was if my understanding was correct because I was taught that f(x)=x²+15x+50 means we inputted x into f, f squared the input added 15 times the input and added 50. What you're saying is different . Every answer I get is different . Which is it.

Yes, your understanding is correct, and f(x)=x²+15x+50 means we inputted x into f, f squared the input added 15 times the input and added 50. For example f(2)=2^2+15*2+50=84. So if the input is x=2, the output will be 84. What different answer are you getting?

Because a lot of other people and you aswell tell me it means for any value of x you input in f he output will be calculated using the expression x²+15x+50 that makes no sense because you just said that I was right that it meant that we plugged x in f,f squared it added 15 times it and added 50. Those two definitions don't match

The formula "x²+15x+50" means that you squared the input added 15 times the input and added 50. So both you and other people who say you should use this formula are correct. They are essentially the same thing, but written in different ways.

Could you please explain how they're the same , look at what I said it makes no sense for them to be the same , my definition is saying we input x , f does something to x and outputs something . Your definitions says for any input we use x²+15x+50 to get the output those are two different things

The formula x²+15x+50 is exactly what the function f does to the inout. Indeed x²+15x+50 = (squared the input)+ (5 times the input)+ (Add 50) You are saying the righthand side of the above inequality, and the formula just give you the left hand side. Think about the above equality for a few seconds, it should help you understand it. I suggest you to evaluate f(2), when the input is , using both your way and the formula. Using wither way, you will get 84.

I meant "when the input is 2"

Whatever it doesn't make sense I'm just gonna stop trying .

Also idk why you're talking about inequalities

Sorry, I meant the equality x²+15x+50 = (squared the input)+ (5 times the input)+ (Add 50).

Idk why what you're saying doesn't make sense , how can two thing different explanations be the same I'm so confused

I strongly suggest you to you to evaluate the out put for x=2, using both your way and the formula. Using wither method, you will get 84. Just try it. You will learn a lot by doing it, and it should make it much more clear.

I think you keep asking questions, without taking the time to think about my answers. Try computing f(2) using both explanations.

My way just says for any input you square it add 15 times it and add 50 the way you explain. Yours is like x²+15x+50 is just a fixed formula given to you instead of showing what f does to x to understand what it does to any number I hope you understand. I know how to plug in a value , I learned that in 8th grade

The formula "x²+15x+50" means square it (here it means the input x) add 15 times it and add 50.

The whole point of my question was to understand the relationship between my definition your definition and if we did f(2) we get 84 when we plug in x we get x²+15x+50 so x²+15x+50 is the result of plugging in x into f or is it the formula to calculate any x. It's all so confusing I hope you understand that I'm trying my hardest to understand this, I've been trying for weeks and can't seem to find an answer if x²+15x+50 is the result why do we set the result equal to 0. I'm trying I swear.

Now you are changing the question again! You have two different questions. 1- The first question should be clear by my last comment: The formula "x²+15x+50" means square it (here it means the input x) add 15 times it and add 50. 2- Why do we set the result equal to 0? I answered this in the comments I added at the end of my answer.

I didn't change the question , that was my original question . You refuse to understand what I'm asking and keep reverting back to your generic text book answer like that's gonna help me. If I tell you I've been trying to understand this for week obviously it means I've read all those answers . Plugging in 2 isn't gonna help because I already mention I've solved hundreds of these if had actually read my questions instead of rushing an answer. Actually read what I'm asking .

To be honest, if reading my comments didn't help you, nothing will. I suggest you to carefully read my comments again.

Also note that there is nothing deep here. Your question is kind of shallow, and should take about take about a few minutes to be settled/understood.

Shallow huh.

Yes, and you are hearing this from someone with a PhD who has taught calculus for over 20 years.

Appreciate it

I'm sorry for asking this again but just so I can stop thinking about it. f(x)=x²+15x+50 means f squared x added 15 times x then added 50. I'm sorry for repeating it, I just want to get it off my mind once and for all.

Yes, exactly.

Thank you for answering me,and for taking the time out of your day.

No problem. Note that x^2 means square it, 15x meaning multiply it by 15, +50 means add 50 to it. So what you were saying is the same as computing x^2+15x+50.

Yes , but I was just specifically talking about what f does to x, x²+15x+50 is the result of applying f to x. I was just asking what were the steps f was doing to x

If you get what I'm saying . I was specifically taking about x as an input and what f does to it. It squares it adds 15 times it and then adds 50 , and we get the result x²+15x+50 , if it's f(3) instead of doing all those steps I mentioned to x it would be to 3. I hope you understand what I'm saying .

You kinda confused me with your last message because x²+15x+50 is the result after applying the function f to x but ok

Sir, I think you are over complicating and over thinking this. Applying f to x, and evaluating the expression x²+15x+50, plugging x in f, they are all the same thing. There is nothing deep or complicated here. My suggestion is you accept that all those mean the same thing and move on. I have also spent over 2 hours answering your question and comments for only $14! I reside in USA where the minimum wage is 15$.

I'm sorry I will stop , thank you .

If after all these comments you have a slightly better understanding. You may try to make your question very clear and concise, and post another question. Thanks for the tip, and good luck :)