Find the domain for each of the following functions. Give your answer in interval notation.

Question

Find the domain for each of the following functions. Give your answer in interval notation.

a. f(x) =(x-1)/(x^(2)-4)

b. g(x) = sqrt(3-x) + (x)/(2x-1)

Please Help Solve!

Answer 1

a. The denominator cannot be zero, so the domain excludes where x² - 4 = 0. This means x ≠ 2 and x ≠ -2. So the domain is (-∞, -2) U (-2, 2) U (2, ∞).

b. Here we want 3 - x ≥ 0 since we are taking the square root of it and also 2x - 1 ≠ 0 since it is in the denominator. These simplify to x ≤ 3 and x ≠ 1/2. So the domain is (-∞, 1/2) U (1/2, 3].