Asked by tee
Find the domain of the function algebraically and support the answer graphically h times x equal the square root of 4-x squared divided by x - 3
Answers
Answered by
Steve
That's <u>h of x</u>, not h times x.
h(x) = √(4-x^2)/(x-3)
or
h(x) = √((4-x^2)/(x-3))
In either case, x=3 is excluded because the denominator is zero.
Now, √z has a domain of z>=0.
In the first case, 4-x^2 >= 0, so x^2 <= 4
|x| <= 2
In the second case, check the domain is (-∞,-2]U[2,3).
See whether you can determine why.
h(x) = √(4-x^2)/(x-3)
or
h(x) = √((4-x^2)/(x-3))
In either case, x=3 is excluded because the denominator is zero.
Now, √z has a domain of z>=0.
In the first case, 4-x^2 >= 0, so x^2 <= 4
|x| <= 2
In the second case, check the domain is (-∞,-2]U[2,3).
See whether you can determine why.
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