Question

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

i’m in S5 (i think equivalent to year 12 and 11th grade) and this is higher maths

Answer 1

Answer: i) 1 - 9x² - 12x

ii) 17 - 3x²

iii) - 20 + 10x² - x⁴

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