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 inverse of A is A itself since A is an involutory matrix.

The inverse of A is (1/det(A)) * adj(A) = (1/-2) * [[4, -2], [-3, 1]] = [[-2, 1], [1.5, -0.5]].

The area of the triangle can be calculated as (1/2) * base * height. The area is 30 cm² (since it's a right triangle). Using area = (1/2) * 12 * height, we find height = 5 cm.

Using the area formula, Area = 1/2 * base * height. The area can also be calculated using Heron's formula, which gives 24. Thus, height = (2 * Area) / base = (2 * 24) / 10 = 4.8.

Using the area formula, Area = 1/2 * base * height. First, find the area using Heron's formula, then use it to find the height.

Diagonal length = √[(3-0)² + (4-0)²] = √[9 + 16] = √25 = 5.

The diameter is twice the radius, so 2 * 7 = 14.

The radius is √16 = 4, so the diameter is 2 * radius = 8.

The length of the latus rectum is given by (2b^2/a). Here, b^2 = 16, a^2 = 36, so length = (2*16/6) = 12.

The length of the latus rectum of the ellipse is given by 2a^2/b.

The length of the latus rectum of a parabola given by the equation y^2 = 4px is 4p. Here, 4p = 12, so p = 3. Therefore, the length of the latus rectum is 4p = 12.

The length of the latus rectum of the parabola y^2 = 4ax is 4a.

The length of the latus rectum of the parabola y^2 = 8x is 4.

Length = √[(2 - (-1))² + (3 - (-1))²] = √[3² + 4²] = √25 = 5.

Length = |5 - 2| = 3.

Median length m_a = 1/2 * √(2b^2 + 2c^2 - a^2) = 1/2 * √(2*8^2 + 2*10^2 - 6^2) = 1/2 * √(128 + 200 - 36) = 1/2 * √292 = 7.

The x-intercept is (4, 0) and the y-intercept is (0, 3). The length of the segment is sqrt((4-0)^2 + (0-3)^2) = sqrt(16 + 9) = 5.

As x approaches infinity, (1/x) approaches 0.

Using L'Hôpital's Rule, lim (x -> 1) (x^2 - 1)/(x - 1) = lim (x -> 1) (2x)/(1) = 2.

As x approaches 0 from the right, f(x) approaches infinity, indicating a discontinuity at x = 0.

Magnitude = √(2^2 + (-3)^2 + 6^2) = √(4 + 9 + 36) = √49 = 7.

Magnitude = √(3^2 + 4^2) = √(9 + 16) = √25 = 5

Magnitude |C| = √(6^2 + 8^2 + 10^2) = √(36 + 64 + 100) = √200 = 10√2.

Magnitude of v = √(3^2 + (-4)^2) = √(9 + 16) = √25 = 5.