Fucntions

[moneyman]

For which of the following functions is f(a+b)=f(a)+f(b) for all positive numbers a and b??

f(x)=x^2

f(x)=x+1

f(x)=sq.rt x

f(x)=2/x

f(x)=-3x

OA is E

[joshi.komal]

Hi moneyman,


To solve this problem lets take the each option one by one:

1 ) f(x)=x^2
f(a) = a^2 F(b)=b^2 F(a + b)=(a+b)^2
a^2 + b^2 not = (a+b)^2
INCORRECT

2) f(x)=x+1
f(a) = a+1 f(b)=b+1 f(a + b)=(a+b)+1
(a+1) +( b+1) not = (a+b +1)
INCORRECT

3 ) f(x)=sq.rt x
f(a) = sq.rt a f(b)=sq.rt b f(a + b)=sq.rt (a+b)
sqrt (a) + sqrt ( b) not = sqrt (a+b)
INCORRECT

4) f(x)=2/x
f(a) = 2/a f(b)=2/b f(a + b)=2/(a+b)
2/a +2/b not = 2/(a+b)
INCORRECT

5) f(x)=-3x
f(a) = -3a f(b)=-3b f(a + b)=-3(a+b)
-3(a) + (-3)( b) = -3(a+b)
-3(a+b) = -3(a+b)
CORRECT

And so OA is E.

Hope it helps

Thanks
Komal

[senthil]

The best way wud be just take a sample number and substitute in the fuctions and u will get the answer !

Answer is E


Thanks
Senthil

[Kaunteya]

The best way would be just take a sample number and substitute in the fuctions and u will get the answer !

Answer is E


Thanks
Senthil

Hey Senthil, what do you mean take a sample number? If f(x)=-3x how does that correlate with f(a+b). Could explain a bit furthur in detail. Thanks mate.

[senthil]

f(a+b)=f(a)+f(b)

Take f(5) =f(2)+f(3) , it adheres to the conditions give in the problem.

thereby going with each options ,
f(x)=x^2

f(5) = f(2)+f(3)
25 = 4 + 9 Therefore first function ruled out !

f(x)=x+1
f(5) = f(2)+f(3)
6 = 3 + 4 Does not satisfy

similarly f(x)=sq.rt x ,f(x)=2/x

f(x)=-3x
f(5) = f(2)+f(3)
-15 = -6 + -9 Satisfies can even cross check with some other number too..


Hope its clear !

Thanks
Senthil

[Kaunteya]

Roger, thanks man. That helps!

Kaunteya