Question

3A. Explain in your own words how to find the domain of a function if you know its equation.B. Find the domain of f (x) =9-7X6x2413x-15Be sure to show relevant work.

Answer 1

The domain of a function is the complete set of possible values of the independent variable.

In plain English, this definition means:

The domain is the set of all possible x-values that will make the function "work" and will output real y-values.

When finding the domain, remember:

The denominator (bottom) of a fraction cannot be zero

The number under a square root sign must be positive in this section

In general, we determine the domain of each function by looking for those values of the independent variable (usually x) which we are allowed to use. (Usually, we have to avoid 0 on the bottom of a fraction or negative values under the square root sign).

For example,

Find the domain of

`f\mleft(x\mright)=\frac{\sqrt[]{x+2}}{x^2-9}`

In the numerator (top) of this fraction, we have a square root. To make sure the values under the square root are non-negative, we can only choose values of x greater than or equal to -2.

The denominator (bottom) has x²-9 which we recognize we can write as(x+3)(x−3). So our values for x cannot include−3 (from the first bracket) o3 (from the second).

We don't need to worry about the −3 anyway, because we decided in the first step that x≥−2.

So the domain for this case is x≥−2,x≠3, which we can write as (−2,3)∪(3,∞).