functions

 

  1. what the gf(4) means = g(f(4))
  2. work out the most inner one (f(4))

f(4) = 3(4) - 5 = 7

  1. substitute answer into next bracket, 7 into g, g(7) because f(4)=7
  2. solve next bracket

g(7) = 2x+4 = 2(7) +4 = 14+4 = 18

 q1

(f(g(3)))

g(3) = x^2 - 5 = 3^2 - 5 = 9-5 = 4

f(4) = 2(4) + 5 = 13

 q2

g(f(3))

f(3) = 5(3) -9 = 15-9 = 6

g(6) = 6^2+1 = 36+1 = 37

 q3

f(g(x))

just substitute the whole equation into it g into f

fg(x) = (2x+1)^2 + 4

fg(x) = 4x^2 +4x + 5

 q4

  1. do g(f(x))

= 3(2x+3) -1

= 6x +9 - 1

= 6x + 8

  1. make it equal to h(x)

h(x) = 6x + 8

  1. find the inverse function, make it equal to y and make x the subject

y = 6x + 8

y - 8 = 6x

(y-8) / 6 = x

  1. swap the x and y

y = (x-8) / 6

  1. make it equal to what the question is asking

h^-1 (x) = (x-8)/6