Find the Domain of a Function
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Find the domain of following: (i) $f(x) = x^2 - 6$
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Hello! Today we are going to find the domain of the function given in the image.
Finding the Domain of a Function
The function we are looking at is f of x equals x squared minus six.
When finding the domain of a function, we are looking for all possible real values of x for which the function produces a real output.
What is the Domain?
The set of all possible input values ($x$) for which the function is defined.
In mathematics, we usually watch out for two main restrictions: denominators cannot be zero, and the values under a square root cannot be negative.
| Restriction | Example |
|---|---|
| No division by zero | $1/x \implies x \neq 0$ |
| No negative in even roots | $\sqrt{x} \implies x \geq 0$ |
Let's examine our specific function, f of x equals x squared minus six. Does it have a denominator with a variable or a square root symbol?
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