Question

If `h(x)=(f(x))/(g(x))` and `f(x)=3x-1`, how do you determine g(x) given `h(x)=1/(x+9)`?

Answer 1

`g(x)=3x^2+26x-9`

Explanation:

`"given "h(x)=(f(x))/(g(x))" then"`

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

`color(white)(g(x))=(3x-1)/(1/(x+9))`

`color(white)(g(x))=(3x-1)xx(x+9)/1`

`color(white)(g(x))=(3x-1)(x+9)larrcolor(blue)"expand using FOIL"`

`color(white)(g(x))=3x^2+27x-x-9`

`color(white)(g(x))=3x^2+26x-9`