Question

Select functions f and g such that the ratio of function f to function g is equal to the function h.

Answer 1

What is required is that our choice should satisfy the equation:

`f(x)\text{ = g(x) }*\text{ h(x)}`

By observation and trial, we obtain :

`\begin{gathered} g(x)=x^2\text{ - x -2} \\ h(x)\text{ = x - 4} \end{gathered}`

When we multiply, we have:

`\begin{gathered} (x^2\text{ - x - 2) (x -4)} \\ =x^3-4x^2-x^2\text{ + 4x - 2x + 8} \\ =x^3-5x^2\text{ + 2x + 8} \end{gathered}`

Hence,

`f(x)=x^3-5x^2\text{ + 2x + 8}`

In summary,

`\begin{gathered} f(x)=x^3-5x^2\text{ + 2x + 8} \\ h(x)\text{ = x - 4} \\ g(x)=x^2\text{ - x -2} \end{gathered}`