The function f is defined by f(x) = - 1/x for all nonzero numbers x.

Question

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= ?

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

Bunuel · Accepted Answer

Given:  f(x)=-\frac{1}{x} .

As  f(a)=-\frac{1}{a}=-\frac{1}{2}  then  a=2 , also as  f(ab)=-\frac{1}{ab}=\frac{1}{6}  then  ab=-6  -->  2b=-6  -->  b=-3 .

Answer: D.

BrentGMATPrepNow · Answer

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

anshumishra · Answer

f(a) = -1/a = -1/2 => a=2
f(ab) = -1/ab = 1/6 => ab = -6 => b = -6/a = -6/2 = -3

Hence, D.

PareshGmat · Answer

f(x) = \frac{-1}{x}  ; so  x = \frac{-1}{f(x)}

f(a) = \frac{-1}{2} ; so  a = \frac{-1}{\frac{-1}{2}} = 2

f(ab) = \frac{1}{6} ; so  ab = \frac{-1}{\frac{1}{6}} = -6

b = \frac{-6}{2} = -3

Answer = D

msk0657 · Answer

Given f(x) = -1/x.

f(a) = -1/2 , then a has to be - 2.

Now we are asked to b from find f(ab) = 1/6.

In order to make positive ab = 6, this results when a = -2 then b has to be - 3.

Option D is correct answer.

target760gmat · Answer

f(x) = -1/x for all non zero numbers x.If f(a) = -1/2 and f (ab) = 1/6, then b= ?

We can say that a = 2 which fits into the definition of f(x) , f(2) = -1/2.

Similarly, f(ab) = - 1/ (ab) = - 1/ (-6) .

So ab = -6 and a = 2 .

Therefore b= -3.

ANS : D

msk0657 · Answer

Hey, if ab = -6 then b has to be -3 not 3 when a = 2 . Just change it as per your solution .

duahsolo · Answer

Given that f(x) = -1/2 and f(a) = -1/2, then f(a) =-1/a=-1/2 ===> a=2, then backsolve using the answer choices:

f(ab) = f(2b) = 1/6
A) 3 ===> f(2*3) = f(6) = -1/6 
B) 1/3 ===> f((2*1/3) = f(2/3) = -1/(2/3) = -3/2 
C) -1/3 ===> f(2*-1/3) = f(-2/3) = -1/(-2/3) = 3/2
D) -3 ===> f(2*-3) = f(-6) = -1/-6 = 1/6 WINS
E) -12 ===> f(2*-12) = f(-24) = -1/-24 = 1/24

Answer: D

AbdurRakib · Answer

Given, if f(a)= \frac{-1}{2} ,then a=2 
 if f(ab)= \frac{1}{6} = \frac{-1}{-6} ,then ab=-6

Since a=2,so b= \frac{-6}{2} =-3

Correct Answer D

SamBoyle · Answer

Here is how to do the answer broken down. A good video explaining function notation is here https://www.youtube.com/watch?v=T6-Zdr5w_bE .

Basshead · Answer

f(x)= -\frac{1}{x}

f(a) = -\frac{1}{2}

a = 2

f(ab) = \frac{1}{6}

ab = -6

2b = -6
b = -3

Answer is D.

BrushMyQuant · Answer

f(x)= -\frac{1}{x}

=>  f(a)= -\frac{1}{a} = -\frac{1}{2}  (given)
=> a = 2

f(ab) = -\frac{1}{ab} = \frac{1}{6} 
=> ab = -6
=> 2 * b = -6
=> b =  \frac{-6}{2}  = -3

So,  Answer will be D 
Hope it helps!

Watch the following video to learn the Basics of Functions and Custom Characters

https://www.youtube.com/watch?v=b7JoMX0gk8M

bumpbot · Answer

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The function f is defined by f(x) = - 1/x for all nonzero numbers x.

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