776
Answer Key
1.24 . f −1 ( x ) = 2 x
⎨ y | y ≠2 ⎫ ⎭ ⎬ .
−1 is { x | x ≠3}. The range of f −1 is ⎧ ⎩
x −3 . The domain of f
1.25 .
1.26 . The domain of f −1 is (0, ∞). The range of f −1 is (−∞, 0). The inverse function is given by the formula f −1 ( x ) =−1/ x . 1.27 . f (4) =900; f (10) = 24, 300. 1.28 . x / ⎛ ⎝ 2 y 3 ⎞ ⎠ 1.29 . A ( t ) =750 e 0.04 t . After 30 years, there will be approximately $2, 490.09. 1.30 . x = ln3 2 1.31 . x = 1 e 1.32 . 1.29248 1.33 . The magnitude 8.4 earthquake is roughly 10 times as severe as the magnitude 7.4 earthquake. 1.34 . ( x 2 + x −2 )/2 1.35 . 1 2 ln (3) ≈ 0.5493. Section Exercises
1 . a. Domain = {−3, −2, −1, 0, 1, 2, 3}, range = {0, 1, 4, 9} b. Yes, a function 3 . a. Domain = {0, 1, 2, 3}, range = {−3, −2, −1, 0, 1, 2, 3} b. No, not a function 5 . a. Domain = {3, 5, 8, 10, 15, 21, 33}, range = {0, 1, 2, 3} b. Yes, a function 7 . a. −2 b. 3 c. 13 d. −5 x −2 e. 5 a −2 f. 5 a +5 h −2 9 . a. Undefined b. 2 c. 2 3 d. − 2 x e 2 a f. 2 a + h 11 . a. 5 b. 11 c. 23 d. −6 x +5 e. 6 a +5 f. 6 a +6 h +5 13 . a. 9 b. 9 c. 9 d. 9 e. 9 f. 9 15 . x ≥ 1 8 ; y ≥0; x = 1 8 ; no y -intercept
17 . x ≥−2; y ≥−1; x =−1; y =−1+ 2 19 . x ≠4; y ≠0; no x -intercept; y = − 3 4 21 . x >5; y >0; no intercepts 23 .
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