Wed June 13, 2012 By: Ratik Mahajan

Find the domain and range of the following function: 1/sqrt(9-x square)

Expert Reply
Mon June 18, 2012
f(x)= 1/sqrt(9-x square)
To find the domain, we should exclude the points
(a) where the denominatoir = 0
(b) the denominator sqrt(9-x^2) < 0
Now x = +3, -3 doen not lie in the domain since it will make the denomainator zero and hence the function undefined.
For x = 4 and -4 we see that the denomiantor becomes negative of squareroot, which is an imaginary number.
Thus domain of the function 1/sqrt(9-x square) is -3<f(x)<3
Always remember in this case you will have open points at x=3 and -3 since the function is undefined at those points.

Range is the set of all possible y values or values of  1/sqrt(9-x square).

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