sandy wrote:

For which of the following functions f(x) is \(f(a + b) = f(a) + f(b)\)?

(A) \(f(x) = x^2\)

(B) \(f(x) = 5x\)

(C) \(f(x) = 2x + 1\)

(D) \(f(x) =\sqrt{x}\)

(E) \(f(x) = x - 2\)

One approach is to let a = 1 and b = 1 and plug in the values.

So, the question becomes, "Which of the following functions are such that f(1 + 1) = f(1) + f(1)?"

In other words,

for which function does f(2) = f(1) + f(1)?A) If f(x) = x², does f(

2) = f(

1) + f(

1)?

Plug in to get:

2² =

1² +

1²

No, doesn't work

So, it is

not the case that f(

2) = f(

1) + f(

1), when f(x) = x²

ELIMINATE A

B) If f(x) = 5x, does f(

2) = f(

1) + f(

1)?

Plug in to get: 5(

2) = 5(

1) + 5(

1)

It works. KEEP B for now.

C) If f(x) = 2x + 1, does f(

2) = f(

1) + f(

1)?

Plug in to get: 2(

2) + 1 = 2(

1) + 1 + 2(

1) + 1

No, doesn't work

So, it is

not the case that f(

2) = f(

1) + f(

1), when f(x) = 2x + 1

ELIMINATE C

D) If f(x) = √x, does f(

2) = f(

1) + f(

1)?

Plug in to get: √

2 = √

1 + √

1 No, doesn't work

So, it is

not the case that f(

2) = f(

1) + f(

1), when f(x) = √x

ELIMINATE D

E) If f(x) = x - 2, does f(

2) = f(

1) + f(

1)?

Plug in to get:

2 - 2 = (

1 - 2) + (

1 - 2)

No, doesn't work

So, it is

not the case that f(

2) = f(

1) + f(

1), when f(x) = x - 2

ELIMINATE E

By the process of elimination, the correct answer is B

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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