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

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

Option E because

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