Two functions, f and g are defined as f(x) = (2x + 1)/(3x), g(x) = 5x – 3. Find: (g o f)(2) and (f o g)(2)

JAMB Mathematics 2024 281 views
Source: JAMB · 2024

Two functions, f and g are defined as f(x) = (2x + 1)/(3x), g(x) = 5x – 3.

Find: (g o f)(2) and (f o g)(2)

  1. (g o f)(2) = 5/6, (f o g)(2) = 6/7
  2. (g o f)(2) = 7/6, (f o g)(2) = 5/7 ✓
  3. (g o f)(2) = 5/6, (f o g)(2) = 5/7
  4. (g o f)(2) = 7/6, (f o g)(2) = 2/3
Explanation

(g o f)(2) means g(f(2)). f(2) = (4 + 1)/6 = 5/6. Then g(5/6) = 5 × 5/6 − 3 = 25/6 − 18/6 = 7/6.

(f o g)(2) means f(g(2)). g(2) = 10 − 3 = 7. Then f(7) = (14 + 1)/21 = 15/21 = 5/7.

So (g o f)(2) = 7/6 and (f o g)(2) = 5/7.

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