Given information:

The given function is,

  h(x)=1x2−5x4

Concept used:

To represent the function:

A function f is a rule that assigns to each element x in a set D exactly one element called f(x) in a set E. The set D and E are sets of real numbers. The set D is called the domain of the function.

If f is a function with domain D .

Then the set of ordered pairs are.

  {(x, f(x))|x∈D}

The given function is

  h(x)=1x2−5x4

The fourth root a negative number is not allowed (as a real number)

That h(x) is not defined when x2−5x≤0

The domain of h consists of all value of x such that

  x2−5x≤0x2−5x>0x(x−5)>0

There are two conditions,

First condition,

  x>0

And,

  x−5>0x>5

Second condition,

  x<0

And,

  x−5<0x<5

Hence, the domain of h is

  {x∈R|x≠0, x≠5}

Therefore the domain of h is the interval,

  (−∞, 0)∪(5, ∞)