If f(x)=4x+1 and g(x)=kx+2 such that fog(x)=gof(x), then what is the value of k?
- A. 7 ✓
- B. 5
- C. 4
- D. 3
Correct Answer: A. 7
Explanation
Compute the composition f(g(x)) = 4(kx+2) + 1 = 4kx + 9. Then, compute g(f(x)) = k(4x+1) + 2 = 4kx + k + 2. Equating the two expressions gives 4kx + 9 = 4kx + k + 2. This simplifies to k + 2 = 9, which implies k = 7.
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