Question

Mathematics question:

Answer 1

(g/f)(x) = x²-6 / 3x+1 , x ≠ -1/3.

Explanation:

From question statement , we observe that

Two functions are given and we have to find their ratio.

f(x) = x+1 and g(x) = x²-6

(g/f)(x) = ?

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

Putting the values of g(x) and f(x) to above formula,we get

(g/f)(x) = x²-6 / 3x+1

If 3x+1 = 0 ⇒ x = -1/3 then function is undefined.

Hence, (g/f)(x) = x²-6 / 3x+1 , x ≠ -1/3 which is the answer.

Answer 2

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

Explanation:

f(x) = 3x+1

g(x)= x^2- 6

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

Now we plug in g(x) and f(x)

we are given with g(x) and f(x)

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

We cannot factor and simplify it

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