The derivative of \( y = \tan^{-1}(x) \) is \( \frac{1}{1+x^2} \).

The function is undefined at x = 2, so the domain is all real numbers except 2.

The function is undefined at x = 3, so the domain is x ≠ 3.

The expression under the square root must be non-negative, so x - 1 >= 0, hence x >= 1.

The intersection of two sets includes only the elements that are present in both sets. Here, the intersection is {2, 3}.

To find the inverse, set y = 2x + 3, solve for x: x = (y - 3)/2.

To find the inverse, set y = 2x + 5, solve for x: x = (y - 5)/2, thus f^-1(x) = (x - 5)/2.

To find the inverse, set y = 3x + 1, solve for x: x = (y - 1)/3.

To find the inverse, set y = 3x + 4, solve for x: x = (y - 4)/3, hence the inverse is (x - 4)/3.

To find the inverse, set y = 3x - 5, solve for x: x = (y + 5)/3, hence f^(-1)(x) = (x + 5)/3.

The total number of subsets is 2^n = 2^2 = 4. Proper subsets exclude the set itself, so there are 4 - 1 = 3 proper subsets.

The empty set has exactly one subset, which is itself (∅).

The number of subsets of a set with n elements is 2^n. Here, n = 3, so 2^3 = 8.

The number of subsets of a set with n elements is 2^n. Here, n = 5, so 2^5 = 32.

The number of subsets of a set with n elements is 2^n. Here, n = 5, so the number of subsets is 2^5 = 32.

The number of subsets of a set with n elements is 2^n. Here, n = 4, so the number of subsets is 2^4 = 16.

The number of subsets of a set with n elements is 2^n. Here, n = 4, so the number of subsets is 2^4 = 16.

The power set of a set is the set of all its subsets. For A = {a, b}, the power set is {∅, {a}, {b}, {a, b}}.

The power set of the empty set contains only the empty set itself: {∅}.

The power set of F = {a} is {∅, {a}}.

The power set of G = {1} is {∅, {1}}.

The power set of a set with n elements has 2^n elements. For {1, 2}, the power set is {∅, {1}, {2}, {1, 2}}.

cot^(-1)(0) = π/2

sec^(-1)(2) = π/3, since sec(π/3) = 2.

The function is a downward-opening parabola with a maximum value of 4, so the range is (-∞, 4].

The function f(x) = x^2 has a minimum value of 0, so its range is [0, ∞).

The range of sin^(-1)(x) is (-π/2, π/2).

The sum of the roots of ax^2 + bx + c = 0 is -b/a. Here, sum = 5.

The sum of the roots is given by -b/a = 5/1 = 5.

The sum of the roots is given by -b/a = 5/1 = 5.