What is the domain and range of h(x)=-sqrt(x^2-16) -3h(x)=−√x2−16−3?

1 Answer
Shwetank Mauria
Dec 29, 2017

Domain for h(x)h(x) is x<=-4x≤−4 and x>=4x≥4. Range for h(x)h(x) is (-oo,-3)(−∞,−3).

Explanation:

It is apparent that x^2-16>0x2−16>0, hence we must x<=-4x≤−4 or x>=4x≥4 and that is the domain for h(x)h(x).

Further the least value for sqrt(x^2-16)√x2−16 is 00 and it can up to oo∞.

Hence range for h(x)=-sqrt(x^2-16)-3h(x)=−√x2−16−3 is from a minimum of -oo−∞ to maximum of -3−3 i.e. (-oo,-3)(−∞,−3).

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