Join the growing community of curious minds on IDNLearn.com and get the answers you need. Discover thorough and trustworthy answers from our community of knowledgeable professionals, tailored to meet your specific needs.
Sagot :
Solution:
Given:
[tex]\begin{gathered} f(x)=3x+5 \\ g(x)=x^2 \end{gathered}[/tex][tex]\frac{g(x)}{f(x)}\frac{}{}=\frac{x^2}{3x+5}[/tex]The domain of a function is the set of input values for which the function is defined.
The function will be undefined when the denominator is 0.
Hence, we test for singularity or undefined points.
[tex]\begin{gathered} \frac{g(x)}{f(x)}\frac{}{}=\frac{x^2}{3x+5} \\ Equating\text{ the denominator to 0;} \\ 3x+5=0 \\ 3x=-5 \\ x=-\frac{5}{3} \\ \\ Hence,\text{ singularity or undefined point exists at }x=-\frac{5}{3} \end{gathered}[/tex]Thus, the domain will exist at all other values except the singularity or undefined point.
Hence, the domain is;
[tex]x<-\frac{5}{3}\text{ OR }x>-\frac{5}{3}[/tex]Thus, the final answer is;
[tex]\frac{x^2}{3x+5};\text{ domain is the set of all real numbers except }-\frac{5}{3}[/tex]OPTION D is correct
Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Your questions deserve reliable answers. Thanks for visiting IDNLearn.com, and see you again soon for more helpful information.
