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Pg. 136/150 Homework

Pg. 136/150 Homework. Pg. 136 #10 – 34 even Pg. 150 #45 – 49 all #9 True #27 Circle r = 2, C(0, 2) #11 True #29 f -1 ( x ) = x 2 + 2 #13 f ( g ( x ) = g ( f ( x ) = x D:[0, ∞), R:[2, ∞) #15 f ( g ( x ) = g ( f ( x ) = x #31 f -1 ( x ) = ½( x ) – (5/2)

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Pg. 136/150 Homework

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  1. Pg. 136/150 Homework • Pg. 136 #10 – 34 evenPg. 150 #45 – 49 all • #9 True #27 Circle r = 2, C(0, 2) • #11 True #29 f -1(x) = x2 + 2 • #13 f(g(x) = g(f(x) = x D:[0, ∞), R:[2, ∞) • #15 f(g(x) = g(f(x) = x #31 f -1(x) = ½(x) – (5/2) • #17 No, it fails the HLT #33 f -1(x) = (2x + 3)/(x – 1) • #19 No, it fails the HLT #35 f -1(x) = x2 – 2 • #21 Yes, it passes the HLT #42 (a) 450 – 15x = rent • #23 No (b) 1900+20x =tenants • #25 Where they meet #43 [0, 30) on the line y = x #44 x = 0, rent = $450

  2. 2.7 Inverse Functions Pg. 150 #42 – 44 #42 – Money and people stick together. That’s why there are two equations: 450 – 15x = rent 1900 + 20x = tenants #43 – Revenue is the number of tenants times the cost of rent, or those two equations multiplied. So, R = (450 – 15x)(1900 + 20x). Set each piece equal to zero and you know you’re boundaries. x = 0 and x = 30, so [0, 30) because you don’t want R = 0. #44 – Graph R in your calculator and find the maximum. It will occur when x = 0 and R = 450*1900. • A large apartment rental company has 2500 units available, and 1900 are currently rented at an average of $450/mo. A market survey indicates that each $15 decrease in average monthly rent will result in 20 new tenants.

  3. 2.7 Inverse Functions Inverse Relations Inverse Functions In order for an inverse function to exist, first you must be dealing with a function and that function must pass the VLT and the HLT. Functions and Inverse Functions can be composed together to prove they are inverses of each other. Their result will always be x. • The point (a, b) is in the relation R if, and only if, (b, a) is in the relation R-1. • Graphically, an inverse is a reflection of the original graph over the line y = x.

  4. 2.7 Inverse Functions Examples Find the inverse of f(x) = -x3 algebraically. Graph the original equation and the inverse along with the line y = x to show it has the proper symmetry. • Find the inverse of y = ½ x – 3 algebraically. • Graph the original equation and the inverse along with the line y = x to show it has the proper symmetry.

  5. 2.7 Inverse Functions Inverse Functions Show that g(x) = will have an inverse function. Find the inverse function and state its domain and range. Prove that the two are actually inverses. Will h(x) = x3 – 5xhave an inverse function? • Show that f(x) = will have an inverse function. • Find the inverse function and state its domain and range. • Prove that the two are actually inverses.

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