Theory question 115
Algebraic Expressions(a) Find the image of (−2, 4) under the mapping (x, y) → (2x, y − 3x).
(b) Two functions f and g are defined as: f: x → x2/4 − 9, g: x → 1/2x (x ≠ 0). (i) Evaluate f(4) + g(−1/3). (ii) If f × g = 2, solve for x.
Show the model answer
Model answer
(a) (2(−2), 4 − 3(−2)) = (−4, 10).
(b)(i) f(4) = 16/4 − 9 = −5; g(−⅓) = 1/(−⅔) = −3/2. Sum = −6½.
(ii) (x2/4 − 9) × 1/(2x) = 2 → (x2 − 36)/(8x) = 2 → x2 − 16x − 36 = 0 → (x − 18)(x + 2) = 0 → x = 18 or x = −2.
Explanation
f × g means multiply the two expressions.