MathRevolution wrote:

[

Math Revolution GMAT math practice question]

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

\(A. f(x)=x+1\)

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

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

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

\(E. f(x)=2^x\)

Another approach is to

test each function to see whether f(a+b) = f(a)f(b)

For example, let's see what happens if

a = 1 and

b = 1So, with each function, is it true that f(

1 +

1) = f(

1)f(

1)?

In other words, is it true that f(

2) = f(

1)f(

1)?

A. f(x) = x + 1

Is it true that f(

2) = f(

1)f(

1)?

Plug values into the function to get:

2 + 1 = (

1 + 1)(

1 + 1)

Simplify: 3 = 4

No good.

ELIMINATE A

B. f(x) = x² + 1

Is it true that f(

2) = f(

1)f(

1)?

Plug values into the function to get:

2² + 1 = (

1² + 1)(

1² + 1)

Simplify: 4 + 1 = (2)(2)

Simplify: 5 = 4

No good.

ELIMINATE B

C. f(x) = √x

Is it true that f(

2) = f(

1)f(

1)?

Plug values into the function to get: √

2 = (√

1)(√

1)

Simplify: √2 = (1)(1)

No good.

ELIMINATE C

D. f(x) = 1/x

Is it true that f(

2) = f(

1)f(

1)?

Plug values into the function to get: 1/

2 = (1/

1)(1/

1)

Simplify: 1/2 = (1)(1)

No good.

ELIMINATE D

By the process of elimination, the correct answer is E

Cheers,

Brent

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