Which of the following functions satisfies f(a + b) = f(a)*f(b)

Question

Which of the following functions satisfies  f(a+b)=f(a)*f(b)  for all positive numbers a and b ?

A.  f(x)=x+1

B.  f(x)=x^2+1

C.  f(x)=\sqrt{x}

D.  f(x)=\frac{1}{x}

E.  f(x)=2^x

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Rabab36 · Answer

a=2 b=2
F(2+2)= f(2)*f(2)
4=4

only option E satisfy this 
2^2 =4

option E correct

m not sure about this

sumit99kr · Answer

Let a=b=x
From the given equation, f(x+x)=f(x)*f(x)
So, f(2x) = (f(x))^2
Now check the value of f(2x) in all the options and see which one satisfies the above relation.
A. f(2x) = 2x + 1, and f(x)^2 = (x+1)^2, Since both will not be same hence INCORRECT

B. f(2x) = (2x)^2 + 1, and f(x)^2 = (x^2+1)^2, Since both will not be same hence INCORRECT

C. f(2x) = (2x)^1/2, and f(x)^2 =x, Since both will not be same hence INCORRECT

D. f(2x) = 1/2x , and f(x)^2 = 1/x^2, Since both will not be same hence INCORRECT

E. f(2x) = 2^(2x), and f(x)^2 = (2^x)^2= 2^(2x), Since both are same hence CORRECT

sujoykrdatta · Answer

We need to check the options: 
Option A: f(x) = x + 1
=> f(a) = a + 1 and f(b) = b + 1 => f(a) * f(b) = (a + 1)(b + 1) = ab + a + b + 1
f(a+b) = a + b + 1 => Clearly, f(a + b) is NOT equal to f(a) * f(b)

Clearly, Option B would not satisfy either

Option C: f(x)= \sqrt{x} 
=> f(a) =  \sqrt{a}  and f(b) =  \sqrt{b}  => f(a) * f(b) =  \sqrt{ab} 
f(a+b) =  \sqrt{a+b}  => Clearly, f(a + b) is NOT equal to f(a) * f(b)

Option D: f(x) = 1/x
=> f(a) = 1/a and f(b) = 1/b => f(a) * f(b) = 1/ab
f(a+b) = 1/(a + b) => Clearly, f(a + b) is NOT equal to f(a) * f(b)

Option E: f(x) =  2^x 
=> f(a) =  2^a  and f(b) =  2^b  => f(a) * f(b) =  2^a * 2^b  =  2^(a+b) 
f(a+b) =  2^(a+b)  => Clearly, f(a + b) IS equal to f(a) * f(b)

Answer E

Loopmonkey · Answer

Option E because

2^(a+b)=2^a*2^b

findingmyself · Answer

I’m taking A=2 and B=1
Evaluating answer choice B
F(2)=5
F(1)=2
F(3)=5*2=10
F(3)=3^2+1=10
Both are matching. Why then option B is not correct?

Which of the following functions satisfies f(a + b) = f(a)*f(b)

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GMAT Problem Solving (PS) Questions

Which of the following functions satisfies f(a + b) = f(a)*f(b)

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