Advanced MathHardShifting the input of an exponential function by a half
Advanced Math practice question
The function f is defined by f(x) = 4ˣ. Which expression is equal to f(x + 1/2) for all x?
- A. 2 · 4ˣCorrect
- B. 4ˣ + 2
- C. 4ˣ / 2
- D. 16ˣ
Answer: A. 2 · 4ˣ
f(x + 1/2) = 4^(x + 1/2) = 4ˣ · 4^(1/2) = 2 · 4ˣ.
Why the other answers are wrong
- B. 4ˣ + 2
- Adding to the exponent multiplies the value; it doesn't add to it.
- C. 4ˣ / 2
- 4^(1/2) = 2 multiplies, not divides.
- D. 16ˣ
- 16ˣ = 4^(2x), which doubles the exponent rather than adding 1/2.
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