If f(a*b) = f(a) + f(b), what is the value of f(1)?

Question

If  f(a*b) = f(a) + f(b) , what is the value of  f(1) ?
 
A. 1 
B. -1 
C. 0 
D. 2 
E. -2

vishujn2 · Answer

f(A*B)=F(A) +F(B)
TAKE A=2 AND B=1
F(2*1)=F(2). +F(1)
F(1)=0

VirenSingh · Answer

F(a * b ) = f(a) * f(b)
find f(1) = ?

Lets take a = 1 and b any number 0, 1, 2...

for 0 --> f(1 * 0 ) = f(1) + f(0) = f(1) = 0

for 2 --> f(1 * 2 ) = f(1) + f(2)
 f(2) = f(1) + f(2)
 f(1) = 0
Answer C

Sonia2023 · Answer

chetan2u  - How would you approach this question? I am unable to understand what concept/logic this question is trying to test.

chetan2u · Answer

Sonia2023 , I will not get into too much depth of functions, but what would suffice for GMAT is that function is a relationship between input and output. You give an input and you get a related output. 
In maths, we generally talk in terms of x and y. 
So if y=3x+2…..input is x and output you will get is y. 
x=2, y=8 or x=0, y=2 and so on.

Now what do you do with these values? 
You can draw the points as coordinates in X-Y plane.

Now this y is nothing but f(x). So, y=f(x)=3x+2.
f(1) = 3*1+2 =5 and similarly values for other f(2) etc can be found.

Let us get back to the question. 
f(a*b) = f(a)+f(b)
So, it tell us that when you substitute x as the product of two numbers, it is equal to sum of values of functions when the values are put separately. 
if we take f(x) as 3x+2, f(a*b)=3(a*b)+2
So 3ab+2=3a+2+3b+2……3ab=3(a+b)+2
But we do not know exactly what f(x) is.

Here we are dealing with f(1)?
So, surely one of a or b should be 1 to get f(1).
f(a*1)=f(1)+f(a)
You can take b also as 1 => f(1*1)=f(1)+f(1)…..f(1)=f(1)+f(1)….f(1)=0
Or, you solve f(a*1)=f(1)+f(a) to get f(1)=0

lesgooo · Answer

Hi  chetan2u ,
great solution with simple words. I used a different approach please let me know if that is correct?
f(ab) = f(a) + f(b)
f(a) = f(ab) - f(b)
f(a) = f(b) (a-1)
f(1) = f(b) (1-1)
f(1) = f(b) 0
f(1) = 0

chetan2u · Answer

Hi, I dont think that will be correct...
Yoi can not write f(a*b)-f(a) as f(a)(f(b)-1)...
Say f(x) = x^2-2x
Now f(a*b)-f(a) = (ab)^2-2ab-(a^2-2a)
While f(a)(f(b)-1) =(a^2-2a)(b^2-2b-1)

If f(a*b) = f(a) + f(b), what is the value of f(1)?

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If f(a*b) = f(a) + f(b), what is the value of f(1)?

Prep Toolkit

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