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C3 finding the range

14835282760091516752987.jpg are my ranges for g(x) right ? One of them doesn't match the answer thanks

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(edited 7 years ago)
Reply 1
Original post by coconut64
14835282760091516752987.jpg are my ranges for g(x) right ? One of them doesn't match the answer thanks

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The first range is right.
(edited 7 years ago)
Reply 2
Original post by solC
The first range is right.
g(x)<-7 is unnecessary since -7<8 anyway


So-7 is also right ? Thanks
Reply 3
Original post by coconut64
So-7 is also right ? Thanks


In fact, that second one is wrong because, even with the first range, g(x)<-7 doesn't make sense because there are clearly values between -7 and 8 as seen from the graph.
Ignore what I first said, sorry.
Reply 4
Original post by solC
In fact, that second one is wrong because, even with the first range, g(x)<-7 doesn't make sense because there are clearly values between -7 and 8 as seen from the graph.
Ignore what I first said, sorry.


The second equation -x^2+3 has a domain of x>3 , so surely the range has to be less than -7
Reply 5
Original post by coconut64
are my ranges for g(x) right ? One of them doesn't match the answer thanks


Both your answers are correct. What were the answers given?

EDIT : Wrong, ignore.
(edited 7 years ago)
Reply 6
Original post by solC
In fact, that second one is wrong because, even with the first range, g(x)<-7 doesn't make sense because there are clearly values between -7 and 8 as seen from the graph.
Ignore what I first said, sorry.

Are you looking at the correct graph?

You should be looking at the graph of y=x2+7y=-x^2+7 restricted to x>3x>3.

Coconut64 has drawn it correctly.

EDIT: Wrong, ignore.
(edited 7 years ago)
Reply 7
Original post by notnek
Are you looking at the correct graph?

You should be looking at the graph of y=x2+7y=-x^2+7 restricted to x>3x>3.

Coconut64 has drawn it correctly.



The answer given was g(x)<=8, so I assumed that they treated the whole thing as a single function.
Reply 8
Original post by coconut64
are my ranges for g(x) right ? One of them doesn't match the answer thanks


I just noticed you posted the answers in your OP. Can you also post a picture of the actual question i,e, a photograph of the textbook?
Reply 9
Original post by notnek
I just noticed you posted the answers in your OP. Can you also post a picture of the actual question i,e, a photograph of the textbook?


1483536058179-2016494093.jpg
Reply 10
Original post by coconut64
are my ranges for g(x) right ? One of them doesn't match the answer thanks


Ignore what I've said so far. I just looked at your question again and noticed that g(x) is a single function. This is not two separate functions.

Did you realise that?
(edited 7 years ago)
Reply 11
Original post by solC
The answer given was g(x)<=8, so I assumed that they treated the whole thing as a single function.

It is a single function - I read the question incorrectly.

So you're correct, sorry :smile:
Reply 12
Original post by notnek
It is a single function - I read the question incorrectly.

So you're correct, sorry :smile:


So if the questions are laid out like this gx then 2 equations , there is only one function so only one range should be given? But there are 2 domains though...
Reply 13
Original post by coconut64
So if the questions are laid out like this gx then 2 equations , there is only one function so only one range should be given? But there are 2 domains though...

The function is equal to 3x13x-1 for x3x\leq 3 and equal to x2+7-x^2+7 for x>3x>3.

So the domain of the function is actually all real numbers. It's just defined differently over different parts of the domain but it's a single function.

The range of the function is the set of values that f can be over the full domain. So in your graph, it's anything that y can be.

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