Composition of Two Functions L151 A) ff(x) = x + 1 g(x) = 5x ^ 2 and h(x) = - 6 find the following. 1) g(f(x)) = 5 * (f(x)) ^ 2 f(f(x)) = 5 * (f(x)) ^ 1 g( f(x) = 5 * (x + 1) ^ 2 = x(5x + 10) + 5 2) f(h(x)) (5x + 10) + 5 -5 B) If f(x) = 7 g(x) = 2x and h(x) = - 3x - 8 find the following. 1) (f g) (x) 2) (h g) (x) 7 - 6x - 8 C) f(x) = 8x - 1 g(x) = x find the following. 1) (g f' )(x) 2) (f g) (x) 6x - 1 8x - 1 3) Is (f g) (x) =(g f)(x); true D) 1) f(x) = - x + 15 and g(x) = 2x ^ 2 + 9 which of the following represents f(g(x)) int) - 2x ^ 2 + 6 ii) - 2x - 24 iii) 2x + 24 iv) - 2x ^ 2 - 6 2) If g(x) = 6x and h(x) = 10 which of the following represents (g h) (x) * 7 Name: Wind Date: Period: COMPOSITE FUNCTION WORKSHEET Directions: Show all work for credit. Work must be neat and answer must be circled. For 1-9: Let f(x) = 2x - 1 g(x) = 3x and h(x) = x ^ 2 + 1 Compute the following: 1. f(g(- 3)) 3(- 3) = 3(- 3) = - 9 f(- q) * (plus/minus (- Psi)) - 1 =(E( Psi) 2. f(h(7)) m(7) = (1) ^ n + 1 = 49 + 1 = 50 F(50) + 2(50) -1(=+9) 3. (g^ * h) (24) h(Eu) = (1u) ^ 2 + 1 =<=76+1=577 9(\$11)= 3(57) = 5(0, 3) 4. f(g(h(2))) n(2j=(2)^ * + i = 4 + 1 = 5 J(5) = 3(5) = 15 F(15) = x\{5\} - (1629) 5. h(g * (f * (5))) f(5) = 2(5) - 1 = 10 - 1 * 9 5(4) = 3(9) = 27 h * (27) ^ 2 + t = 729 + 1 plus/minus 7360 6. g(f(h(- 6))) h(- 6) =(-6)^ 2 + t = 3k + 1 = 33 6 lfloor37 rfloor=2\ 37 rfloor-1= 7d -1 equiv73 5(73) = 3(73) 7. f(x + 1) \mathfrak{G}(x + j) = \mathfrak{L}\{x + j\} - 1 8. g(3a) 5(3a) = (3a) . h(x - 2) ln(n - 2) = (n - 2) ^ 2 + 1 -2)+1 For 10-11: Let f(x) = - 3x + 7 and mathfrak gr * (x) = 2x ^ 2 - 8 . Compute the following: 10. f(g(x)) = - 3(2x ^ 2 - 8) + 7 = - 6x ^ 5 - 2d + 7 11. (g ^ n * f)(x) = 2 * (- 3x + y) ^ 2 - 8 = 2(- 3n + 1)(- 3n + 7) - 8 = 2(4n ^ 3 - 2) =-21n^ prime prime +4n)-8 = z(4x ^ 4 - 42x + 44) - g -353^ =\$ 4x + 90% ) 12. If f(x) = 3x - 5 and g(x) = x ^ 2 find (f g) (3) 9(3)=( 30 ^ 2 - 9 F(9) = 3(9) - 5 = 22 ) 13. If f(x) = - 9x - 9 and g(x) = sqrt(x - 9) find (f g) (10) 9(10) = sqrt(10 - 4) = sqrt(i) = 1 f(1) = - 9(1] - 9 = - 9 - 9 = - 15 )

Composition of Two Functions

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