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# C3 Functions

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Need help in part 8(c), how do we get the range over here as 0<f(x)<4? I tend to get confused when finding the range and domain of such situations. Could anyone tell me how to do so? TIA.
2. (Original post by sabahshahed294)

Need help in part 8(c), how do we get the range over here as 0<f(x)<4? I tend to get confused when finding the range and domain of such situations. Could anyone tell me how to do so? TIA.
Draw a graph?
For x > 1, the denominator is increasing as x increases, so f(x) is decreasing.
As x tends to infinity, f(x) gets smaller and closer to zero.
Then evaluate f(1).
3. (Original post by EricPiphany)
Draw a graph?
For x > 1, the denominator is increasing as x increases, so f(x) is decreasing.
As x tends to infinity, f(x) gets smaller and closer to zero.
Then evaluate f(1).
So, you simply substituted x=1? Or you came to a conclusion by drawing out a graph?
4. (Original post by sabahshahed294)
So, you simply substituted x=1? Or you came to a conclusion by drawing out a graph?
Yes, substitution. Look at the graph, you don't even need to draw it. x>1 shows that you can ignore the left branch of it and since it is beyond the asymptote, the range will not involve infinity. So you can plug in x=1 and it will be everything between (and excluding including) f(1) and 0.
5. (Original post by RDKGames)
Yes, substitution. Look at the graph, you don't even need to draw it. x>1 shows that you can ignore the left branch of it and since it is beyond the asymptote, the range will not involve infinity. So you can plug in x=1 and it will be everything between (and excluding including) f(1) and 0.
Alright! Thank you.

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