What is the domain and range of f(x) = sqrt(x^2-36)?

1 Answer
Alan P.
Dec 19, 2015

Domain: RR, (-oo,-6] uu [+6,+oo]
Range: RR, [0,+oo)

Explanation:

f(x) is defined in the Real numbers provided
color(white)("XXX")x^2-36 >= 0
This will be true provided
color(white)("XXX")x >= 6color(white)("XX")orcolor(white)("XX")x <=-6
Therefore the domain (in RR) is x in (+oo,-6]uu[+6,+oo)

Since sqrt("any real number") is defined as the principle square root (i.e. >= 0)
the range is f(x) in [0,+oo)

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