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Question 484122: what is the domain and range of the function... f(x)= square root of (x^4-25x^2)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! what is the domain and range of the function... f(x)= square root of (x^4-25x^2)
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Domain is a set of all possible inputs (x-values) for which the function is defined.
Range is a set of all possible outputs (y-values)
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f(x)=√ (x^4-25x^2)
(x^4-25x^2)≥0
x^2(x^2-25)≥0
x^2(x+5)(x-5)≥0
Draw a number line with the zeros on it:
<.....+....-5......-......0......-.....5....+.....>
Explanation for number line:
When x is a large number >5, it can easily be seen that the expression under the radical (the radican) is positive. As you go to the left thru the zeros, the signs of the intervals switch if the zeros are of odd multiplicity (1, 3, 5,etc). 5 and -5 are of multiplicity 1 and 0 of multiplicity 2.
Domain: (-∞, -5] U [5, ∞)
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I don't see any restriction for y.
For each x in the domain, there is a y-value.
Range:(-∞, ∞)
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