Question

Let f(x) = 3x + 5 and g(x) = x^2Find g(x)/f(x) and state it’s domain 3x+5/x^2; domain is the set of real numbers except 0X/8; domain is the set of all real numbersX/3x+5; domain is the set of all real numbers except -5/3 X^2/3x+5; domain is the set of all real numbers except -5/3

Answer 1

Given:

`\begin{gathered} f(x)=3x+5 \\ g(x)=x^2 \end{gathered}`
`(g(x))/(f(x))\frac{}{}=(x^2)/(3x+5)`

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.

Thus, the domain will exist at all other values except the singularity or undefined point.

Hence, the domain is;

`x<-(5)/(3)\text{ OR }x>-(5)/(3)`

Thus, the final answer is;

`(x^2)/(3x+5);\text{ domain is the set of all real numbers except }-(5)/(3)`

OPTION D is correct