SOLUTION: what is the domain and range of the function... f(x)= square root of (x^4-25x^2)

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)
**
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)
..
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, ∞)
..
I don't see any restriction for y.
For each x in the domain, there is a y-value.
Range:(-∞, ∞)
RELATED QUESTIONS
what is the domain and range of the function... f(x)= square root of (9-x^2)/... (answered by chessace)

what is the domain and range of the function f(x)= -25x+900? explain your... (answered by Fombitz)

What is the domain and range of the function f(x)= square root 8-2x? (answered by timvanswearingen)

What is the Domain and Range of f(x)=square root of... (answered by Boreal)

What is the domain and range of the function ... f(x)= square root of (3-x)/(x-2)(x^2+5) (answered by lwsshak3)

what is the domain and range of the function.... f(x)= 4/x +... (answered by lwsshak3)

What is the domain and the range of f(x) = square root of (3x -... (answered by josgarithmetic)

what is the domain of f(x)= x squared minus 9 what is the domain of f(x)=square root... (answered by edjones)

How do you solve domains of functions? For example, f(x)=square root of (x-2)... (answered by lwsshak3)