▶️ Answer/Explanation
Answers:
(a) p = −13 → Substitute g(x) into f(x): fg(x) = f(5x−4) = 4(5x−4) + 3 = 20x − 16 + 3 = 20x − 13.
(b) \( h^{-1}(x) = \frac{3x + 1}{5} \) → Swap x and y, then solve for y: \( x = \frac{5y – 1}{3} \) → 3x = 5y − 1 → y = (3x + 1)/5.
▶️ Answer/Explanation
Answer:
(a) a = 7
(b)(i) 6x – 9 or 3(2x – 3)
(ii) \(\frac{x-7}{2}\)
Explanation:
(a) Substitute x=-2: 3(-2)² + a = 19 → 12 + a = 19 → a=7
(b)(i) gh(x) = g(h(x)) = 2(3x-8)+7 = 6x-9
(ii) Swap x and y: x=2y+7 → y=(x-7)/2
(a) Substitute x=-2: 3(-2)² + a = 19 → 12 + a = 19 → a=7
(b)(i) gh(x) = g(h(x)) = 2(3x-8)+7 = 6x-9
(ii) Swap x and y: x=2y+7 → y=(x-7)/2