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

1 Answer
bp
Sep 25, 2015

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

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

Explanation:

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}#

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