SOLUTION: Find the range of this function f(x) defined over the largest possible domain.
x + 1/x
I tried to do this by completing the square by multiplying out the x at the bottom. So
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-> SOLUTION: Find the range of this function f(x) defined over the largest possible domain.
x + 1/x
I tried to do this by completing the square by multiplying out the x at the bottom. So
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Question 937605: Find the range of this function f(x) defined over the largest possible domain.
x + 1/x
I tried to do this by completing the square by multiplying out the x at the bottom. So I got:
x^2 + 1 = 0
(x+1/2)^2 -1/4 = 0
So f(x) > 1/4
But the textbook says f(x) < or equal to -2
or f(x) > or equal to 2.
I really need help on how to get to these answers. Answer by josgarithmetic(39618) (Show Source):
You can put this solution on YOUR website! f(x)=x+1/x is ambiguous. Further it is not a quadratic function. You can get better help asking for what you exactly want and giving the full problem description.
Some clarification given:
like , which was exactly as you wrote. Sometimes students want the x+1 grouped as a separate expression but omit the grouping symbols.
The allowed values for x must be , so that y will be undefined for x at 0.
You wanted to find the range. Think what happens to y very near to 0 on the left and on the right. ....
.... UNBOUNDED negative as x approaches 0 from the left, and unbounded positive as x approaches 0 from the right.
Without further algebra, although you might want it,... I skip ahead to a graph.
A derivative might be needed to find the rest of the range restriction.
THIS MEANS YOU ARE OR HAVE STUDIED CALCULUS 1. ( I cannot think of another way).
WHERE is this derivative equal to 0? or
Note from the sketch of the graph you might make, x=-1 will give a local max, and x=1 will give a local min. Use your given function definition to find those function values. The range must EXCLUDE the values between f(-1) and f(1).
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