The calculated domain of the function f(x) = (x + 1)(x³ - x)⁻¹/(x² + 2) is x ≠ 0 and x ≠ 1 i.e. the set of all real numbers except 0 and 1
How to determine the domain of the function
From the question, we have the following parameters that can be used in our computation:
f(x) = (x + 1)(x³ - x)⁻¹/(x² + 2)
This can be expressed as
f(x) = (x + 1)/(x³ - x)(x² + 2)
To calculate the domain, we set the denominator not equal to 0
So, we have
(x³ - x)(x² + 2) ≠ 0
This gives
x²(x - 1)(x² + 2) ≠ 0
Split
x² ≠ 0, x - 1 ≠ 0 and x² + 2 ≠ 0
When solved for x, we have
x ≠ 0 and x ≠ 1
Hence, the domain of the function is x ≠ 0 and x ≠ 1