Question

Find (f/g)(x) for the following functionsf(x) = 10x3- 12x2 + 6x - 7 g(x)=-14x2-1

Answer 1

We have two functions, f(x) and g(x) and we have to find (f/g)(x).

Let h(x) = (f/g)(x).

We can write it like this:

`h(x)=(f(x))/(g(x))=(10x^3-12x^2+6x-7)/(-14x^2-1)=(-10x^3+12x^2-6x+7)/(14x^2+1)`

(f/g)(x) is defined for all x but g(x)=0.

We can find the values of x for which (f/g) is not defined as:

`\begin{gathered} -14x^2-1=0 \\ -14x^2=1 \\ x^2=-(1)/(14) \\ x=\sqrt[]{-(1)/(14)}\longrightarrow\text{not a real number} \end{gathered}`

So we can conclude that (f/g)(x) is defined for all real numbers.

Answer: (f/g)(x) = (-10x^3+12x^2-6x+7)/(14x^2+1)