I think solving for x will require solving a quartic equation, so that probably won't work well.
I would try sketching the graph, using the derivative and other tools to find local maxima or minima, which can be put together to find the range.
Hello. Good job, but you've got a bit more work to do, on that domain. So far, your result shows all values that won't lead to zero in the function's denominator. Next, you need to eliminate values that make the numerator undefined. For example, what happens if you try to evaluate the function for x=-4?… This is what i came up with for the domain …
Next, you need to eliminate values that make the numerator undefined. For example, what happens if you try to evaluate the function for x=-4?
Are you allowed to use calculus, for finding the range? If not, I'm wondering whether you're allowed to technology (like a graphing calculator) or a numerical method, to approximate a solution for the range.
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Maybe I am wrong about calculus not being allowed. I don't think the answer is wanted as a decimal as we are putting it into interval notation.Hmm...without the calculus it will be more difficult to analytically find the range...
Oh, good. You can zoom in on that local maximum point (between x-values -2/3 and 1/2).… graphing calculators are allowed.
Looks good to me, but I would replace the 'equal to' sign in the range statement to \(\displaystyle \approx\) because the decimal number is approximated.
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W|A gives an value of:
[MATH]y=\frac{9\sqrt{23+\sqrt{1969}}}{911-23\sqrt{1969}}\approx-0.674095748943020[/MATH]
for that local maximum in the middle.