Finding the Domain

Q:  Find the domain of h(x):

h(x) = 27 / (3-x)

A:  The domain represents all of the possible x values.  The best way to find the domain is to first think of what numbers x cannot be.

There are a few areas of concern when we think about domains… We need to check

  • Denominators
  • Square-roots
  • Logarithms

So, looking at the function: h(x) = 27 / (3-x)

We know that the denominator cannot equal zero in any expression.  So,

(3-x) ≠ 0

-x ≠ – 3

x ≠ 3

Therefore, x can be anything except -3.

If written in interval notation, this is: (-∞, -3) U (-3, ∞).

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