SOLUTION: Find a and b. If 2 < x < 4, then a < 1/(x - 6) < b.

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Question 1207693: Find a and b.

If 2 < x < 4, then a < 1/(x - 6) < b.
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!
2 < x < 4

Substitute the greatest lower bound of x, which is 2  1/(2-6) = -1/4 
and the least upper bound of x, which is 4.   1/(4-6) = -1/2

Since 1/(x-6) is continuous and decreasing for x < 6, it's approaching -1/2 from
below as x approaches 4 from the left, and approaching -1/4 as x approaches 2
from the right,  

-1/2 < 1/(x - 6) < -1/4 

Edwin
Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


On the given interval 2 < x < 4, the function 1/(x-6) is monotonic, so the maximum and minimum values of the function on that interval are at the endpoints of the interval.

x=2; 1/(x-6)=1/(-4)=-1/4

x=4; 1/(x-6)=1/(-2)=-1/2

Note that the function value is less ("more negative") at x=4, so the function value at x=4 is the lower end of the range of function values.

ANSWER: a=-1/2,b=-1/4;

i.e., -1/2 < 1/(x-6) < -1/4
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