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Math Help - range

  1. #1
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    range

    the range of function
    f(x)=tan(2sqrt(x-4)+sqrt(6-x)) is

    i know x is (-pi/2,pi/2)
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  2. #2
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    e^(i*pi)'s Avatar
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    Do you see why the domain is x - 4 \geq 0 and 6-x \geq 0?

    The range will be between these two points
    Last edited by e^(i*pi); June 10th 2011 at 10:06 AM. Reason: edits being sloooooooooooooow
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  3. #3
    A Plied Mathematician
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    Quote Originally Posted by prat
    the range of function
    f(x)=tan(2sqrt(x-4)+sqrt(6-x)) is

    i know x is (-pi/2,pi/2)
    This is quite a subtle problem, in my opinion. You must solve the problem in two fairly complicated overall steps. Let

    f(x)=2\sqrt{x-4}+\sqrt{6-x}.

    You must first find the domain and range of this function. That's step 1. Step 2 is to use the range of this function as the domain of the tangent function, and see if there are any further restrictions. Can you see your way forward?
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