HELP! Function Notation!!

Part 1:

Well, if f(x) = 1 – 6x, and f(x) = 0, then it would be logical to conclude that 1 – 6x = 0.

This solves to give:

Spoiler

Part 2:

If you put 2x into the function instead, this will happen:
f(2x) = 1 – (6 × 2x)
f(2x) = 1 – 12x.
So it would thus follow, that you could say that, as your answer:

Spoiler

(edited 9 years ago)

Reply 2

superbear

OP

Thanks for the reply, I kind of undesrstand it now, do you know the name of the second part so i can google it to try and get some questions becasue i can not find any sources of questions or videos on this?

Original post by danconway

Part 1:

Well, if f(x) = 1 – 6x, and f(x) = 0, then it would be logical to conclude that 1 – 6x = 0.

This solves to give:

Spoiler

Part 2:

If you put 2x into the function instead, this will happen:
f(2x) = 1 – (6 × 2x)
f(2x) = 1 – 12x.
So it would thus follow, that you could say that, as your answer:

Spoiler

Reply 3

MangoFreak

17

Original post by Old_Simon

Part 1 above by danconway IMHO is wrong.

Why would you say that? It's correct.

Reply 4

Original post by Old_Simon

Part 1 above by danconway IMHO is wrong.

Is it really now?

Reply 5

MangoFreak

17

Original post by superbear

Thanks for the reply, I kind of undesrstand it now, do you know the name of the second part so i can google it to try and get some questions becasue i can not find any sources of questions or videos on this?

If a function is defined as f(x) = x that means you can replace x on the right-hand side with whatever is in the brackets on the left-hand side.

So f(x) = 2x

f(3) = 2 x 3

The functions don't need to be f(x) = x, they could be defined as f(y) = y or f(t) = t etc. but it will usually be f(x).

Reply 6

Original post by Old_Simon

This is a function not an equation. We do not simply say f(x)=0. It doesn't.

That sounds like rubbish – we do say f(x) = 0.

In fact, the Additional Maths exam I sat yesterday (published by the OCR exam board, who obviously know something about maths) had a question, precisely worded "Solve the equation f(x) = 0."

Functions ARE equations, but instead of getting out, say, y, you get out f(x).

Obviously you might have some superior qualification and tell me that everything I have learnt is rubbish, but I am 100% certain that I solved that function correctly.

Edit: actually, no I won't be courteous – I don't understand why the hell you think I'm wrong. Good day :smile:

(edited 9 years ago)

Reply 7

Maprunner

Original post by Old_Simon

Part 1 above by danconway IMHO is wrong.

Why? I see nothing wrong with it.

In terms of Function Notation, I will try and break it down; I'm sorry if I may come across as patronising, but I don't know exactly how well you understand this topic.

F(x) means a function. In your example, the function is 1 - 6x. This means that the value of the 'x' you put into the F(x) is used in the 1 - 6x part. So if it was F(2), the function would be 1 - (6 * 2) = -11.

If a function is set equal to something, for example F(x) = 0, and you're asked to solve it, you need to find what value of 'x' gives you 0. As shown above, just set the equation equal to the number you're given and rearrange to find the answer. For the second question, you change the 'x' to '2x' and work out what the equation gives you, then simplify down to the form the question asks for if needed.

Hope this helps to clear up any problems you had

(edited 9 years ago)

Reply 8

Original post by Old_Simon

This is a function not an equation. We do not simply say f(x)=0. It doesn't.

How would you do it?

I would normally say:

If f(x)=1-6x, find the value of x when f(x)=0.

Reply 9

Original post by danconway

Functions ARE equations,

Whoa, hold on a second. I agree with your method, but that's definitely not true.

A function is a one to one or many to one relation between two variables.

Reply 10

Original post by Arithmeticae

Whoa, hold on a second. I agree with your method, but that's definitely not true.

Well, to the extent of solving them. Obviously they are very different on other levels.

Reply 11

Original post by Old_Simon

Yes but yr example from your exam is different. In that case f(x) = 0 apparently. In this case we are asked to solve for F(x) =0. Functions are not equations. As already explained in this case you need to substitute x=0 into the function.

Wouldn't that be f(0)? Solve f(x)=0 is a different question altogether.

Reply 12

Original post by Old_Simon

Yes but yr example from your exam is different. In that case f(x) = 0 apparently. In this case we are asked to solve for F(x) =0. Functions are not equations. As already explained in this case you need to substitute x=0 into the function.

Okay, that's a lie. That would be f(0), not f(x) = 0...

Reply 13

superbear

OP

I checked the mark scheme for the question, and you were right. Thanks for your help.

Original post by danconway

That sounds like rubbish – we do say f(x) = 0.

In fact, the Additional Maths exam I sat yesterday (published by the OCR exam board, who obviously know something about maths) had a question, precisely worded "Solve the equation f(x) = 0."

Functions ARE equations, but instead of getting out, say, y, you get out f(x).

Obviously you might have some superior qualification and tell me that everything I have learnt is rubbish, but I am 100% certain that I solved that function correctly.

Edit: actually, no I won't be courteous – I don't understand why the hell you think I'm wrong. Good day :smile:

Reply 14

Original post by danconway

Well, to the extent of solving them. Obviously they are very different on other levels.

They're two completely different things.

If you're solving a function for a specific value, you're forming an equation from that function and working out what value of x gives a certain value when put into that function.

Reply 15

Original post by superbear

I checked the mark scheme for the question, and you were right. Thanks for your help.

Great – got a better understanding of the topic?

Reply 16

StarvingAutist

17

Reading this thread made me cringe

Reply 17

Old_Simon

12

Original post by danconway

Great – got a better understanding of the topic?

Functions are not equations. You are leaving this thread under a fundamental misapprehension. I simply misread something. Good luck anyway.

Reply 18