If a function f is defined by \(f(x)=-\dfrac{1}{x}\) for all nonzero numbers x. If \(f(a)=-\dfrac{1}{2}\) and

[AAPL]

GMAT Prep

If a function f is defined by \(f(x)=-\dfrac{1}{x}\) for all nonzero numbers x. If \(f(a)=-\dfrac{1}{2}\) and \(f(ab)=\dfrac{1}{6}\) then b=?

A. 3
B. 1/3
C. -1/3
D. -3
E. -12

OA D

[Brent@GMATPrepNow]

GMAT Prep

If a function f is defined by \(f(x)=-\dfrac{1}{x}\) for all nonzero numbers x. If \(f(a)=-\dfrac{1}{2}\) and \(f(ab)=\dfrac{1}{6}\) then b=?

A. 3
B. 1/3
C. -1/3
D. -3
E. -12

OA D

Given: f(x) = -1/x

f(a) = -1/2
So, f(a) = -1/a = -1/2
This means that a = 2

f(ab) = 1/6
So, f(ab) = -1/ab = 1/6
This means that ab = -6

If a = 2, and ab = -6, we can see that b = -3

Answer: D