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Bunuel
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Which of the following functions satisfies f(a + b) = f(a)*f(b) 02 Jan 2023, 02:30
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E
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70% (02:01) correct 30% (01:43) wrong based on 223 sessions

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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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E
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Rabab36
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Which of the following functions satisfies f(a + b) = f(a)*f(b) 02 Jan 2023, 03:53
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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
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Which of the following functions satisfies f(a + b) = f(a)*f(b) 02 Jan 2023, 04:17
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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
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Which of the following functions satisfies f(a + b) = f(a)*f(b) 03 Jan 2023, 21:07
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Bunuel
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. \(f(x)=2^x\)
This is a PS Butler Question

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
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Which of the following functions satisfies f(a + b) = f(a)*f(b) 04 Jan 2023, 04:18
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Option E because

\(2^(a+b)=2^a*2^b\)
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Which of the following functions satisfies f(a + b) = f(a)*f(b) 22 May 2025, 23:39
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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?
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