What is the value of \alpha in this function?

Question

What is the value of
`\alpha` in this function?

Answer 1

We have the point:

`\left(-4,\ (7)/(128)\right)`

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

`f(x)=(a)/(x^4)\to y=(a)/(x^4)\\\\\left(-4,\ (7)/(128)\right)\to x=-4,\ y=(7)/(128)\\\\(a)/((-4)^4)=(7)/(128)\\\\(a)/(256)=(7)/(128)\qquad\text{multiply both sides by 256}\\\\a=(7)/(128)\cdot256\\\\\boxed{a=14}`

Answer 2

hello :

the graph passes by ( -4; 7/128) : f(-4) = 7/128

a/ (-4)^4 = 7/128

a / 256 = 7/128

a/2 = 7

a = 14