Find the domain of the function enter your answer in interval notation

f(x)=x^4/x^2+x-72

1 answer

To find the domain of the function, we need to identify all the values of x that make the denominator equal to zero. We can set the denominator equal to zero and solve for x:

x^2 + x - 72 = 0

Factoring this equation, we get:

(x + 9)(x - 8) = 0

Setting each factor equal to zero, we find that x = -9 and x = 8.

Since dividing by zero is undefined, the function is not defined for x = -9 and x = 8.

Therefore, the domain of the function is all real numbers except -9 and 8.

In interval notation, the domain is (-∞, -9) ∪ (-9, 8) ∪ (8, ∞).