Question

find the domain and range of f(x)=√x^2-9
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Answer 1

Answer:

Let's investigate what happens on the interval [3,+∞). We note that the function f(x)=x2−9−−−−−√ is symmetric around x=0, so we can justify not needing to look at the cases when x∈(−∞,−3] to find the range.

For x∈[3,+∞), we have the following:

f(x) is a (strictly increasing) continuous function on this interval

f(3)=0

f(x)→+∞ as x→+∞

Thus we can conclude that the range for f(x) will be all nonnegative real numbers, namely the interval [0,+∞)

Answer 2

Step-by-step explanation:

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