How do you find the domain and range of $f(x)= sqrt(x^4-16x^2)$ ?

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Answer 1 · 2015-09-25T17:23:24

Domain ${x in RR, x=0, x>=4 or x<=-4}$

Range ${y in RR, y>=0}$

Write $f(x)= sqrt (x^2(x-4)(x+4))$

For f(x) to be real , either $x =0, or (x-4)(x+4) >=0$

This implies that either both x-4 and x+4 should be $>=0 or <=0$
which means either $x>=4 or x<=-4$ .

Hence domain would be ${x in RR, x=0, x>=4 or x<=-4}$ . In iterval notation it would be $(-oo,-4]U 0 U[4,oo)$

For range it is clear that for x=0, y=0 and for $x>=4 or x<=-4$ , y would be positive. Thus range would be ${y in RR, y>=0}$

How do you find the domain and range of f(x)= sqrt(x^4-16x^2)f(x)= sqrt(x^4-16x^2)?