Question

Pleaseeeee help asap!!

Answer 1

(D)
`((g)/(f))(x)=(x^(2)-6)/(3x+1), x{\\eq}-(1)/(3)`

Explanation:

Given: f(x)=
`3x+1` and g(x)=
`x^(2)-6`.

To find:
`((g)/(f))(x)`

Solution: Given that f(x)=
`3x+1` and g(x)=
`x^(2)-6`, then applying the operations on the functions f(x) and g(x), we get

`((g)/(f))(x)= (g(x))/(f(x))`, f(x)≠0

`((g)/(f))(x)=(x^(2)-6)/(3x+1)`

Thus,
`((g)/(f))(x)=(x^(2)-6)/(3x+1), x{\\eq}-(1)/(3)`

Hence, option D is correct.

Answer 2

ANSWER


`D. \: \: \frac{ {x}^(2) - 6}{3x + 1} \: ,x \\e - (1)/(3)`



EXPLANATION

The given functions are;



`f(x) = 3x + 1`


and


`g(x) = {x}^(2) - 6`


We want to find


`( (g)/(f) )(x)`


Recall that,



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


This implies that,


`( (g)/(f) )(x) = \frac{ {x}^(2) - 6}{3x + 1}`

The restriction on this function is that, the denominator must not be zero.


Thus


`3x + 1 \\e0`




`\Rightarrow x \\e - (1)/(3)`