Question

For what value(s) of x are the following undefined?
5x^2+x+1 / x^2+4

Answer 1

In Real numbers: none (defined for all real numbers)

In Complex numbers: not defined for x = 2i, -2i

Explanation:

Fraction becomes undefined when the denominator = 0

x² + 4 = 0

Has no real solutions

The fraction is defined for all real values of x

x² + 4 = 0

x² = -4

x = 2i, -2i

The fraction is not defined for x = +/-2i (in Complex Numbers)

Answer 2

NONE

Explanation:

The function 5x^2+x+1 / x^2+4 is defined for all real numbers because the denominator x² + 4 ≠ 0 for all real numbers