Advanced MathVery hardDifference of two compositions
Advanced Math practice question
The functions f and g are defined by f(x) = 2x² and g(x) = x − 1. Which expression is equal to f(g(x)) − g(f(x)) for all x?
- A. −4x + 3Correct
- B. 4x − 3
- C. −4x + 1
- D. 3
Answer: A. −4x + 3
f(g(x)) = 2(x − 1)² = 2x² − 4x + 2 and g(f(x)) = 2x² − 1. Subtracting: −4x + 3.
Why the other answers are wrong
- B. 4x − 3
- 4x − 3 is g(f(x)) − f(g(x)), the reverse order.
- C. −4x + 1
- −4x + 1 comes from 2(x − 1)² = 2x² − 4x + 1, halving the constant wrongly.
- D. 3
- 3 drops the −4x term.
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