University:
Highline College
Course:
MATHP 141 | Precalculus I Plus Extra Support
Academic year:

2022
Views:

114

Pages:

2
Author:

Bidoggia5pt

Workshop #14 1. Simplify using any method. Assume no denominators are zero. (a) (b) 2 6 9 12 2x3 5 4x 15 (c) (d) 1 2 1 5 + − 2 3 1 2 1 x + 1 y x+y 2. (a) Pick values for a and b to show the following statement is false 1 a (b) Simplify 1 a 1 − 1 b 1 + 1 b = a + b. as much as possible. 3. Simplify the following expressions as much as possible (a) (b) 1 x+y − 1 x (c) y 1 2(x+y)+1 − 1 2x+1 x−1 + x1 1 −1 x +x (d) (x − 1 − 2x−1 )−1 · y x 3 4. In functional analysis the the function space Lp is said to be the dual space of Lq if p and q are related as follows: 1 1 + = 1. p q (a) Find p if q = 2. (b) Find q if p = 7. (c) Solve for p in terms of q. 5. Do the following two equations have the same solutions? Why or why not? (a) x2 + 12x + 27 = 0 (b) x + 5 − 26 2x − 8 = x+9 x+9 6. Solve the following assume no denominators are zero. Are there any extraneous solutions? 5 1 x−1 − = x+4 3 x 3 12 (b) 1 = − x − 2 x2 − 4 (a) (c) x(x + 1)−1 − x(x + 3)−1 = 4 x+3 7. A website has a promotional price where new subscribers pay 360 for a set number of months. After this promotional period ends the price per month increases by 5. Now it costs the same price for one less month. (a) Let x be the number of months during the promotional period. Express the price per month during the promotional period as a fraction using x. (b) Express the price per month after the promotional period as a fraction using x. (c) What does the problem say we should get when we subtract our answer to part (a) from our answer to part (b)? (d) How many months did 360 buy before the price increase? Hint: Turn your answer from part (c) into a radical equation and solve.