Greetings!
Let's find the domain of the function.
We were given: f(x) = 9 - 5/(x^4)
The domain of a function is a group of values that are valid within the function. The domain could range from (-∞, ∞)
However, since we have a fraction, there will be a limit to the range of values.
In this case, we will have to find what value the variable "x" can't be.
Since we are analyzing the "5/(x^4)" part of the function, we know that fractions can't have a denominator of 0. This means that the denominator can't equal zero.
x^4 ≠ 0
Solve for "x" by taking the root of both sides of the equations.
x ≠ 0 Therefore x can't equal 0.
This means that the value of "0" will not be in our domain, making our domain from:
(-∞, 0)∪(0, ∞)
The above means that we are including all the values (due to the use of infinity), except for the value 0.
Answer:
(-∞, 0)∪(0, ∞)