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
_________________
Brent Hanneson – Creator of gmatprepnow.com
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