Advanced MathHardProperty of a doubling function
Advanced Math practice question
The function f is defined by f(x) = 2ˣ. Which of the following is true for every value of a?
- A. f(a + 1) = 2·f(a)Correct
- B. f(a + 1) = f(a) + 2
- C. f(a + 1) = f(a)²
- D. f(2a) = 2·f(a)
Answer: A. f(a + 1) = 2·f(a)
2ᵃ⁺¹ = 2·2ᵃ.
Why the other answers are wrong
- B. f(a + 1) = f(a) + 2
- Adding 1 to the exponent multiplies by 2; it does not add 2.
- C. f(a + 1) = f(a)²
- Squaring doubles the exponent, it does not add 1.
- D. f(2a) = 2·f(a)
- 2²ᵃ = (2ᵃ)², not 2·2ᵃ.
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