Advanced MathHardExponential equation with no solution
Advanced Math practice question
The functions f and g are defined by f(x) = 3 · 2ˣ and g(x) = 2ˣ. For which value of x is f(x) = g(x + 2)?
- A. There is no such value of x.Correct
- B. x = 0
- C. x = 2
- D. x = 3
Answer: A. There is no such value of x.
g(x + 2) = 2^(x + 2) = 4 · 2ˣ. Setting 3 · 2ˣ = 4 · 2ˣ gives 3 = 4 after dividing by 2ˣ, which is impossible.
Why the other answers are wrong
- B. x = 0
- At x = 0: f = 3 and g(2) = 4.
- C. x = 2
- At x = 2: f = 12 and g(4) = 16.
- D. x = 3
- At x = 3: f = 24 and g(5) = 32.
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