Question

This is due tomorrow and i have answers but i think ive done it wrong! please help

Answer 1

Answer:  i) 1 - 9x² - 12x

               ii) 17 - 3x²

             iii) - 20 + 10x² - x⁴

Step-by-step explanation:

g(x) = 3x + 2       h(x) = 5 - x²

i) h(g(x))

  h(3x + 2) = 5 - (3x + 2)²

                  = 5 - (9x² + 12x + 4)

                  = 5 - 9x² - 12x - 4

                  = 1 - 9x² - 12x

ii) g(h(x))

   g(5 - x²) = 3(5 - x²) + 2

                 = 15 - 3x² + 2

                 = 17 - 3x²

iii) h(h(x))

   h(5 - x²) = 5 - (5 - x²)²

                 = 5 - (25 - 10x² + x⁴)

                 = 5 - 25 + 10x² - x⁴

                 = -20 + 10x² - x⁴