If a function f is defined by f(x) = - 1x for all non-zero numbers x. If f(a) = - 12 and f(ab) = 16, then b = ?

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PS · Problem Solving

505-555

Functions

If a function $f$ is defined by $f(x) = -\frac{1}{x}$ for all non-zero numbers $x$ . If $f(a) = -\frac{1}{2}$ and $f(ab) = \frac{1}{6}$ , then $b =$ ?

Correct answer marked below

3

\frac{1}{3}

-\frac{1}{3}

-3

Correct

-12

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Comments

AfnanJul 26

Wait, how do you find b from f(ab)=1/6? I got a=-2 from the first part but then I'm stuck.

JohnJul 29

Plug ab into the function: f(ab) = -1/(ab) = 1/6. Then solve for ab, then use a=-2 to get b.

SivamanojAug 23

Is the answer -3? Because f(ab) = 1/6 means ab = -6, and a = -2, so b = 3? Wait no, -6/-2 = 3, but that's choice A. Maybe I messed up a sign.

EnnioSep 4

Check f(a) again: f(a) = -1/a = -1/2 => a = 2. So ab = -6 => b = -3.

JaideepSep 4

Ah, I see. I misread the negative sign. Thanks!

DhruvJun 29

This was pretty straightforward. Just substitute and solve. a=2, then ab=-6, so b=-3. Answer D.

What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.