Question

Let f(x) = 2x-1, g(x) = 3x, and h(x) = x^2 + 1. Compute the following:

1. f(g(-3))
2. fſh(7))
3. (gºh)(24)
4. f(g(h(2)))
5. h(g(f(5))
6. g(f(h(-6)))
7. f(x + 1)
9. h(x-2)
8. g(3a)

Answer 1

The computed values are: 1. -19, 2. 99, 3. 1731, 4. 29, 5. 730, 6. 219, 7. 2x + 1, 8. (x - 2)^2 + 1, 9. 9a.

Step-by-step explanation:

1. To compute f(g(-3)), we first find g(-3) by substituting -3 into the g(x) function: g(-3) = 3*(-3) = -9. Next, we substitute -9 into the f(x) function to find f(g(-3)): f(g(-3)) = 2*(-9) - 1 = -18 - 1 = -19.
2. To compute fſh(7), we first find h(7) by substituting 7 into the h(x) function: h(7) = 7^2 + 1 = 49 + 1 = 50. Next, we substitute 50 into the f(x) function to find fſh(7): fſh(7) = 2*50 - 1 = 100 - 1 = 99.
3. To compute (gºh)(24), we first find h(24) by substituting 24 into the h(x) function: h(24) = 24^2 + 1 = 576 + 1 = 577. Next, we substitute 577 into the g(x) function to find (gºh)(24): (gºh)(24) = 3*577 = 1731.
4. To compute f(g(h(2))), we first find h(2) by substituting 2 into the h(x) function: h(2) = 2^2 + 1 = 4 + 1 = 5. Next, we substitute 5 into the g(x) function to find g(h(2)): g(h(2)) = 3*5 = 15. Finally, we substitute 15 into the f(x) function to find f(g(h(2))): f(g(h(2))) = 2*15 - 1 = 30 - 1 = 29.
5. To compute h(g(f(5))), we first find f(5) by substituting 5 into the f(x) function: f(5) = 2*5 - 1 = 10 - 1 = 9. Next, we substitute 9 into the g(x) function to find g(f(5)): g(f(5)) = 3*9 = 27. Finally, we substitute 27 into the h(x) function to find h(g(f(5))): h(g(f(5))) = 27^2 + 1 = 729 + 1 = 730.
6. To compute g(f(h(-6))), we first find h(-6) by substituting -6 into the h(x) function: h(-6) = (-6)^2 + 1 = 36 + 1 = 37. Next, we substitute 37 into the f(x) function to find f(h(-6)): f(h(-6)) = 2*37 - 1 = 74 - 1 = 73. Finally, we substitute 73 into the g(x) function to find g(f(h(-6))): g(f(h(-6))) = 3*73 = 219.
7. To compute f(x + 1), we substitute x + 1 into the f(x) function: f(x + 1) = 2(x + 1) - 1 = 2x + 2 - 1 = 2x + 1.
8. To compute h(x - 2), we substitute x - 2 into the h(x) function: h(x - 2) = (x - 2)^2 + 1.
9. To compute g(3a), we substitute 3a into the g(x) function: g(3a) = 3(3a) = 9a.