What are the domain and range of the function?

Assuming that     f(x)  =  1 / (3x⁷)

Any  x  value that makes the denominator zero is excluded from the domain.

Let's find any excluded  x  value.

3x⁷  =   0          Divide both sides by  3 .

 x⁷   =   0          Take the  7th  root of both sides.

 x     =   0

So the only excluded  x  value is  0 . So the domain is  (-∞, 0) U (0, ∞)

No matter how big or small of an  x  we plug in,  f(x)  cannot be zero.

The range is (-∞, 0) U (0, ∞)

Here's a graph of the function.