Part A
The domain of a function represents the possible values of x which make the function exist.
hence when finding the domain of a function, the denominator cannnot be zero because it will become undefine and the square root sign must not be negative
Par B
the function given is
[tex]f(x)=\frac{\sqrt[]{9-7x}}{6x^2+13x-15}[/tex]To find the domain, the denominator must not be zero
[tex]\begin{gathered} 6x^2+13x-15=0 \\ 6x^2+18x-5x-15=0 \end{gathered}[/tex][tex]\begin{gathered} 6x(x+3)-5(x+3)=0 \\ (6x_{}-5)(x+3)=0 \end{gathered}[/tex][tex]\begin{gathered} \text{hence} \\ x=\frac{5}{6}\text{ or x=-3} \end{gathered}[/tex]Hence 5/6 and -3 make the function undefine
Also, The function is undefined for all the values of x where
[tex]\begin{gathered} 9-7x<0 \\ 9<7x \\ \frac{9}{7}\frac{9}{7} \end{gathered}[/tex]The function is undefined for all the values of x>9/7
Hence the domain of the function is given by
[tex](-\infty,-3)\cup(-3,\frac{5}{6})\cup(\frac{5}{6},\frac{9}{7})[/tex]Therefore the domain of the function is (-∞ ,-3) U (-3,5/6) U (5/6,9/7)
