iGCSE Mathematics (0580) :E2.13 Understand the idea of a derived function.iGCSE Style Questions Paper 4

(a)(i) 3

Substitute x=2 into f(x): f(2) = 2(2) – 1 = 4 – 1 = 3

(a)(ii) 7

First find f(2)=3 from part (i), then g(f(2)) = g(3) = 3(3) – 2 = 9 – 2 = 7

(b) \(\frac{x + 2}{3}\)

Let y = g(x) = 3x – 2. Swap x and y: x = 3y – 2. Solve for y: 3y = x + 2 → y = (x + 2)/3

(c) 25

j(-2) = 5^-2 = 1/25. Set h(x) = 1/25 → 1/x = 1/25 → x = 25

(d) \(\frac{2x^2 – x – 1}{x}\)

f(x) – h(x) = (2x – 1) – (1/x) = (2x² – x – 1)/x (common denominator)

(e) 2.98 × 10¹⁷

j(2) = 5² = 25. Then j(j(2)) = j(25) = 5²⁵ ≈ 2.98 × 10¹⁷

(f) 625

j^-1(x) = 4 means x = j(4) = 5⁴ = 625