If f(x)=4x+1 and g(x)=kx+2 such that f \circ g(x)=g \circ f(x), then what is the value of k?
- A. 7 ✓
- B. 5
- C. 4
- D. 3
Correct Answer: A. 7
Explanation
Compute the compositions: f(g(x)) = 4(kx+2)+1 = 4kx+9. Next, g(f(x)) = k(4x+1)+2 = 4kx+k+2. Setting them equal gives 4kx+9 = 4kx+k+2. Comparing the constant terms yields k+2=9, which means k=7.
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