Find the domain of the function enter your answer in interval notation
f(x)=x^4/x^2+x-72
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, ∞).
To find the domain of the function f(x) = x^4/(x^2 + x - 72), we need to identify any values of x that would make the denominator equal to zero. This is because division by zero is undefined.
To find those values, we need to solve the equation x^2 + x - 72 = 0.
Factoring the quadratic equation, we have:
(x - 8)(x + 9) = 0
Setting each factor equal to zero, we get:
x - 8 = 0 --> x = 8
x + 9 = 0 --> x = -9
So, the values x = 8 and x = -9 would make the denominator zero.
Therefore, the domain of the function f(x) is all real numbers except for x = 8 and x = -9.
In interval notation, this can be expressed as:
(-∞, -9) U (-9, 8) U (8, ∞)