SOLUTION: Find the domain of the function algebraically f(x)= square root( x^4-16x^2) Work: x^4-16x^2 > or equal to 0 x^2(x^2-16) > or equal to 0 x^2(x-4)(x+4) > or equal to 0

Algebra ->  Functions -> SOLUTION: Find the domain of the function algebraically f(x)= square root( x^4-16x^2) Work: x^4-16x^2 > or equal to 0 x^2(x^2-16) > or equal to 0 x^2(x-4)(x+4) > or equal to 0      Log On


   

Question 898961: Find the domain of the function algebraically f(x)= square root( x^4-16x^2)
Work:
x^4-16x^2 > or equal to 0
x^2(x^2-16) > or equal to 0
x^2(x-4)(x+4) > or equal to 0
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=+sqrt%28+x%5E4-16x%5E2%29
f%28x%29=sqrt%28%28x%5E2%29%28x%5E2-16%29%29
f%28x%29=x%2Asqrt%28x%5E2-16%29
Your work appears on the right track.

x%5E2-16%3E=0
%28x-4%29%28x%2B4%29%3E=0

Critical values for the domain are 4 and -4. Three intervals of the x-axis
can be checked.
You will find the domain is the UNION of highlight%28x%3C-4%29 and highlight%28x%3E4%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Find the domain of the function algebraically f(x)= square root( x^4-16x^2)
Work:
x^4-16x^2 > or equal to 0
x^2(x^2-16) > or equal to 0
x^2(x-4)(x+4) > or equal to 0


That is the CORRECT work!!

At this stage: x%5E2%28x+-+4%29%28x+%2B+4%29+%3E=+0, the CRITICAL POINTS are:

system+%28-+4%2C+0_and%2C+4%29

Based on the critical points, the points and intervals that are solutions to the inequality are:

highlight_green%28highlight_green%28system%28x+%3C=+-+4%2C+x+=+0_and%2C+x+%3E=+4%29%29%29