M19-14

JackSparr0w

To solve this question,

First find the value of f(1/x). To do this, replace x with 1/x in the equation.

so f(1/x)=(1/x)/((1/x)+1) = 1/1+x

Now check which option will give you 1/1+x.

Option A : f(x) = x/x+1 not equal..

Option B : -f(x) = -x/x+1 not equal..

Option C : 1/f(x) = x+1/x not equal..

Option D : 1-f(x) = 1-(x/x+1) =(x+1-x)/x+1 = 1/x+1 .. This is the answer.

Option E : None..


+1 Kudos if this helps..

Thanks! Got it!

For others, I think it may be helpful to elaborate on one other point. After you find that f(1/x) = 1/(1+x), compare this to the answer choices by substituting a value for x.

Ex: (assume x = 2). When x is 2, 1/(1+x) becomes 1/(1+2) or (1/3).

We also know f(x) = x/(x+1) from the question stem. So when x=2, f(x)=2/(2+1), or 2/3. We need to find the answer choice that changes 2/3 to 1/3.

Knowing this we can see that choice D is correct. Choice D is 1-f(x), or 1-(2/3) which equals 1/3; the same as our answer above.

I have reached the substitution but unable to get the process after that...

Hi Tanyanagra,

For me using substitution is better than trying to manipulate the variables, especially under pressure....here's how I solve it !

Substitute x=2 into this 1st equation: f(x) = x divided by x+1 f(2) = 2 divided by 2+1 = 2/3

Then, the question asks what is f(1/x) in terms of f(x)?

You'll need to convert the f(x) to f(1/x) that will be 1/x divided by 1/x+1

Substitute x=2 into this 2nd equation f(1/x): 1/2 divided by 1/2+1 = 1/2 divided by 3/2 = 1/2 * 2/3 = 1/3

Now, you have to find 1/3in the answer choices:

A) f(x) = 2/3 not a match

B) - f(x) = - 2/3 not a match

C) 1/f(x) = 1 divided by 2/3 = 3/2 not a match

D) 1 - f(x) = 1 - 2/3 = 1/3 BINGO!! That's a match

E) none of the above = wrong

I hope it helps!

Thanks Ale!

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

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Hi Bunuel,
It's not given to us that 'x' is not equal to 0 so how can we cancel 'x' when solving for f(1/x)??

If x were 0, 1/x would be undefined and f(1/x) wouldn't make any sense.