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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
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