# Function's domain.Find the domain of the function f(x)=-1/(x+3)(x-3).

justaguide | College Teacher | (Level 2) Distinguished Educator

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The value for any number divided by 0 is not defined. All the values that x can take for which f(x) has a real value is the domain of the function.

Here f(x) = -1/(x+3)(x-3) is not defined when x + 3 = 0 or x - 3 = 0

This gives the domain as R - {-3 , 3}

Matthew Fonda | eNotes Employee

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The domain of a function f(x) is the set of all values of x for which the function is defined.  Since we cannot divide by zero, the function ﻿﻿f(x)=-1/(x+3)(x-3) will be undefined when (x+3)(x-3) = 0. There are two possiblities here: x = -3 and x = +3.

Therefore,

The domain of f(x) = -1 / (x+3)(x-3) is all real numbers except -3 and 3.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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The domain of the function is represented by the interval that contains all the values of x that make the function to exist.
Since the expression of the function is a fraction, then the values of x that cancels the denominator must be rejected out from the domain.
We notice that x = -3 and x = 3 are cancelling out the denominator, therefore the maximum domain of the function is R-{-3 ; 3}.