The domain of u(x) is the set of all real values except 0 and the domain of v(x) is the set of all real values except 2. what are the restrictions on the domain of(u0v)(x)?

the restrictions on the domain of (u°v) (x) are  x ≠ 2 and which v(x) ≠ 0.

Justification:

1) the function (u ° v) (x) is u [ v(x) ], this is, you have to apply first the function v(x) whose argument is (x), and later the function u (v(x) ) whose argument is v(x).

2) So, the domain of the composed function  (u ° v) (x) has to take into account the values for which both functions are defined.

3) The domain excludes x = 2 because v(x) is not defined for x = 2.

4) And the domain must also exclude v(x) = 0 because u is not defined for v(x) = 0.

5) So, in conclusion,  the domain is all the real values except x = 2 and the x for which v(x) = 0.

Therefore the resctrictions are x ≠ 2 and v(x) ≠ 0

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12