Question

Find the domain and solve. For the problem please solve before the end of today.

Answer 1

(-infinity, +infinity)

Step by-step explanation:

Here we're working with a log function. For any base, the domain is x > 0. If we focus on the argument of this particular log function, (1+x^2), we see that log (1+x^2) is defined for all x. No problem if x = 0 here; the "1" in (1+x^2) takes care of that. No problem if x grows very large; the log function can handle it.

Thus, we conclude that the domain of this function is

(-infinity, +infinity). Never mind that this function appears as part of an equation; our job is to find the domain of the logarithmic expression on the left side of the "=" sign.

Answer 2

Answer: Domain is All Real Numbers, x = {1, -1}

Explanation:

log₄² (1 + x²) = 0.25 restriction: 1 + x² ≥ 0 ⇒ x² ≥ -1 ⇒ x = ARN

log₄ (1 + x²) = 0.05

(1 + x²) = 4¹⁾²

1 + x² = 2

x² = 1

x = √1

x = +/- 1