1. f(g(-3)) = f(3*(-3)) = f(-9) = 2*(-9) - 1 = -18 - 1 = -19
2. f(h(7)) = f(7² + 1) = f(49 + 1) = f(50) = 2*50 - 1 = 100 - 1 = 99
3. (g∘h)(24) = g(h(24)) = g(24² + 1) = g(576 + 1) = g(577) = 3*577 = 1731
4. f(g(h(2))) = f(g(2² + 1)) = f(g(4 + 1)) = f(g(5)) = f(3*5) = f(15) = 2*15 - 1 = 30 - 1 = 29
5. h(g(f(5))) = h(g(2*5 - 1)) = h(g(10 - 1)) = h(g(9)) = h(3*9) = h(27) = 27² + 1 = 729 + 1 = 730
6. g(f(h(-6))) = g(f((-6)² + 1)) = g(f(36 + 1)) = g(f(37)) = g(2*37 - 1) = g(74 - 1) = g(73) = 3*73 = 219
7. f(x + 1) = 2(x + 1) - 1 = 2x + 2 - 1 = 2x + 1
8. g(3a) = 3*(3a) = 9a
9. h(x - 2) = (x - 2)² + 1 = x² - 4x + 4 + 1 = x² - 4x + 5
10. f(g(x)) = f(2x² - 8) = -3(2x² - 8) + 7 = -6x² + 24 + 7 = -6x² + 31
11. (g∘f)(x) = g(f(x)) = g(-3x + 7) = 2(-3x + 7)² - 8 = 2(9x² - 42x + 49) - 8 = 18x² - 84x + 98 - 8 = 18x² - 84x + 90
12. (f ∘ g)(3) = f(g(3)) = f(3²) = f(9) = 3*9 - 5 = 27 - 5 = 22
13. (f ∘ g)(10) = f(g(10)) = f(√(10-9)) = f(√1) = f(1) = -9*1 - 9 = -9 - 9 = -18
Parent Tip: Review the logic above to help your child master the concept of composition of functions worksheet.
