Question

Hello I need help with this I’m in a rush thanks

Answer 1

Recall that:

`(f)/(g)(x)=(f(x))/(g(x)),`

and that the domain of a rational function consists of all real numbers such that the denominator is different from zero.

If f(x)=5x+3 and g(x)=4x-5 we get that:

`(f)/(g)(x)=(5x+3)/(4x-5)\text{.}`

The domain of the above rational function is:

`\begin{gathered} \mleft\lbrace x|g(x)\\e0\mright\rbrace=\lbrace x|4x-5\\e0\rbrace \\ =\lbrace x|4x\\e5\rbrace=\lbrace x|x\\e(5)/(4)\rbrace\text{.} \end{gathered}`

Answer: Last option.