What is the value of a ?

Question

What is the value of
`a` ?

Answer 1

We have the point:

`\left(3,\ -(1)/(3)\right)`

Put the coordinates of the point to the equation of the function f:

`f(x)=(a)/(x^3)\to y=(a)/(x^3)\\\\\left(3,\ -(1)/(3)\right)\to x=3,\ y=-(1)/(3)\\\\(a)/(3^3)=-(1)/(3)\\\\(a)/(27)=-(1)/(3)\qquad\text{multiply both sides by 27}\\\\a=-(1)/(3)\cdot27\\\\\boxed{a=-9}`

Answer 2

hello :

the graph passes by ( 3; -1/3) : f(3) = -1/3

a/ (3)^3 = -1/3

a / 27 = -1/3

a/9 = - 1

a = - 9