The function f is defined for all nonzero x by the equation f(x) = x - 1/x. If x ≠0, which of the following equals f(1/x)?
A) f(x)
B) f(-x)
C) f(-1/x)
D) 1/f(x)
E) -1/f(x)
Let x=2.
Then:
f(1/x) = f(1/2).
The question becomes:
Which of the following equals f(1/2)?
Since f(x) = x - 1/x, we get:
f(1/2) = 1/2 - 1/(1/2) = 1/2 - 2 = -3/2. This is our target.
Now plug x=2 into the answers to see which yields our target of -3/2.
A: f(x)
f(2) = 2 - 1/2 = 3/2.
B: f(-x)
f(-2) = -2 - (1/-2) = -3/2.
C: f(-1/x)
f(-1/2) = -1/2 - (1/(-1/2)) = 3/2.
D: 1/f(x)
Since A indicates that f(x) = 3/2, 1/f(x) = 1/(3/2) = 2/3.
E: -1/f(x)
Since D indicates that 1/f(x) = 2/3, -1/f(x) = -2/3.
Our target of -3/2 is yielded only by
B.
The correct answer is
B.
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