Consider the functions given below:
Consider the functions given below:
- A.
(-(1-x))/x2
- B.
1/x2
- C.
(1-x)/x
- D.
(x2)/-(1-x)
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Correct answer: A
Given f(x) = x - 1 and g(x) = (x+1)/x.
Compute f(g(x)): f(g(x)) = g(x) - 1 = (x+1)/x - 1 = 1/x.
Compute g(f(x)): g(f(x)) = g(x-1) = x/(x-1).
Now form the quotient: (1/x) ÷ (x/(x-1)) = (1/x) * ((x-1)/x) = (x-1)/x^2.
Therefore the expression simplifies to - (1-x)/x^2.
Domain note: x ≠ 0 and x ≠ 1, since g(x) requires x ≠ 0 and g(f(x)) requires x ≠ 1.