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# finding the range of a function watch

1. Q. f(x)=1/x+1 , x>3

find the range of f

2. or

??
3. domain is x>3...therefore the range is f(x)<1/4
4. The smaller x is the bigger f is. x>3, so by putting 3 into the equation you can find f<?

x can be any number greater than 3. So 1/x can be small, almost 0. So you know f>1

Oh... thought f(x)=(1/x)+1

Anyway 0<f(x)<1/4
5. (Original post by kosy91)
domain is x>3...therefore the range is f(x)<1/4
how did you work it out??
6. (Original post by Pheylan)

or

??
the first one
7. (Original post by klgyal)
how did you work it out??
do you just stick in x=3 to get 1/4
8. (Original post by klgyal)
do you just stick in x=3 to get 1/4
In this case yes
9. the range is the range of outputs that f(x) can be. In this case the bigger x gets, the smaller F(x) gets. You know the smallest it can be is 3 ( x>3) hence the range is f(x) > 1/4
10. Wouldnt it be 0<f(x)<1/4 ? as f(x) will never reach 0 but will always be less than or equal to 1/4, As x gets large f(x) gets small.
11. What if x = 999, then f(x) = 1/1000.
The greatest value f(x) can take is 1/4, as x>3.
x can be infinitely large, so x+3 tends to infinity, therefore f(x) tends to 0.
So 0 < f(x) =< 1/4, in my opinion.

12. ah i only learnt today, should've been quicker in spotting that lower value as well. Thanks guys!
13. you draw the graph of f(x) where the asymptote is x=-1.

you can now easily get range when domain is x>3

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