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) =19-7x6x2.-13x-15Be sure to show relevant work.

Answer 1

A)

The domain of a function can be found using its rule of correspondence. If it is given as an algebraic equation, then we can analyze the restrictions over the variable of the function.

Those restrictions include that the denominator of an expression cannot be 0, and the radicand of a root with even index cannot be negative. Then, if the variable appears on the denominator of an expression or inside a radical with even index, we can apply those restrictions to find the values which x cannot take.

B)

Analyze each algebraic equation to find the restrictions over the variable x.

1.-

`f(x)=19-7x`

In this case, the variable x has no restrictions. Then, the domain of the function is the set of all real numbers, which can also be written as:

`(-\infty,\infty)`

2.-

`f(x)=6x^2-13x-15`

In this case, the variable x has no restrictions. Then, the domain of the function is the set of all real numbers, which can also be written as:

`(-\infty,\infty)`