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) =9-7x6x2+13x-15Be sure to show relevant work.

Answer 1

Given the function below,

`f(x)=\frac{\sqrt[]{9-7x}}{6x^2+13x-15}`

To find the domain of the function above, we factorise the denominators to find x factors,

`\begin{gathered} \text{Given the denominator,} \\ 6x^2+13x-15 \end{gathered}`

Factorising the denominator,

`\begin{gathered} 6x^2+13x-15=0 \\ 6x^2+18x-5x-15=0 \\ 6x(x+3)-5(x+3)=0 \\ (6x-5)(x+3)=0 \\ x+3=0 \\ x=-3 \\ 6x-5=0 \\ 6x=5 \\ x=(5)/(6) \\ x=-3\text{ or }(5)/(6) \end{gathered}`

The domain of a function is the set of all possible values of x, except for x=0.

Hence, the domain of the function is the set of all possible values of x except -3 and 5/6.