Problem Solving

Can anyone help me out on how to approach and solve the following question?

For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?

A. f(x) = x^2

B. f(x) = x+1

C. f(x) = square root of x

D. f(x) = 2/x

E. f(x) = -3x

Thanks in advance!

ruthm_24 wrote:Can anyone help me out on how to approach and solve the following question?

For which of the following functions is f(a+b) = f(a) + f(b) for all positive numbers a and b?

A. f(x) = x^2

B. f(x) = x+1

C. f(x) = square root of x

D. f(x) = 2/x

E. f(x) = -3x

Thanks in advance!

Plug in a=2, b=3.

f(a+b) = f(2+3) = f(5)

Then the question becomes:

For which of the following functions does f(5) = f(2) + f(3)?

Answer choice A:
f(5) = 5² = 25
f(2) = 2² = 4
f(3) = 3² = 9
25 = 4+9 Doesn't work.

Answer choice B:
f(5) = 5+1 = 6
f(2) = 2+1 = 3
f(3) = 3+1 = 4
6 = 3+4 = 7 Doesn't work.

Answer choice C:
f(5) = √5
f(2) = √2
f(3) = √3
√5 = √2 + √3 Doesn't work.

Answer choice D:
f(5) = 2/5
f(2) = 2/2 = 1
f(3) = 2/3
2/5 = 1 + 2/3 Doesn't work.

The correct answer is E.

Answer choice E:
f(5) = -3*5 = -15
f(2) = -3*2 = -6
f(3) = -3*3 = -9
-15 = -6 + -9 Success!

If function f(x) satisfies f(x) = f(x^2) for all x, which of the following must be true?

(A) f(4) = f(2)f(2)
(B) f(16) - f(-2) = 0
(C) f(-2) + f(4) = 0
(D) f(3) = 3f(3)
(E) f(0) = 0

nasir wrote:If function f(x) satisfies f(x) = f(x^2) for all x, which of the following must be true?

(A) f(4) = f(2)f(2)
(B) f(16) - f(-2) = 0
(C) f(-2) + f(4) = 0
(D) f(3) = 3f(3)
(E) f(0) = 0

Option A & E

its B

B) f(16) - f(-2) = 0

f(16) = f(4^2)
f(4) = f ( -2^2)
f(-2)

f(-2)-f(-2)=0