find the domain of f(x) = 1/sqrt(x-3)

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

Given the equation: f(x) =1/sqrt(x-3)

We need to find the domain of f(x).

We know that the domain is all x values such that f(x) is defined.

Since f(x) is a quotient, then the denominator can not be zero.

Also, we notice that the denominator is a square root.

Then (x-3) must be positive values.

==> sqrt(x-3) > 0

==> x-3 > 0

==> x > 3

Then the domain is x = ( 3, inf)

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

f(x) = 1/sqrt(x-3). To find the domain.

The domain of the function f(x) = 1/sqrt(x-3) is the set of all values of x for which the function is defined and is real.

If x is  less than 3, then f(x) can not be real. Therefore the x  must be  greater than or equal to  3 for which f(x) is defined.

Therefore the domain of the function f(x) = 1/sqrt(x-3) is  the set {x : x> = 3}.

Or the domain of the function is the interval (3, infinity).

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