Problem Solving

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

A. f(x)=x squared

B. f(x)=x+1

C. f(x)=square root x

D. f(x)=2/x

E. f(x) = -3x

aj5105 wrote:For which of the following functions is f(a+b) = f(a) +f(b) for all positive numbers a & b?

A. f(x)=x squared

B. f(x)=x+1

C. f(x)=square root x

D. f(x)=2/x

E. f(x) = -3x

IMO : E
put values and check for which option the values satisfies the function.
take a = 2 and b = 3
from E f(5) = -15, f(2) = -6, f(3) = -9.
therefore, f(a+b) = f(a)+f(b)
only, E satidfies the function. hence is the answer.
HTH

A. f(x) = x^2

f(a + b) = (a + b)^2 = a^2 + b^2 + 2ab

f(a) + f(b) = a^2 + b^2.

f(a + b) is not equal to f(a) + f(b)


B. f(x) = x + 1

f(a + b) = a + b + 1

f(a) + f(b) = a + 1 + b + 1.

f(a + b) is not equal to f(a) + f(b)


C. f(x) = sqrt(x)

f(a + b) = sqrt(a + b)

f(a) + f(b) = sqrt(a) + sqrt(b)

f(a + b) is not equal to f(a) + f(b)


D. f(x) = 2/x

f(a + b) = 2/(a + b)

f(a) + f(b) = 2/a + 2/b = 2(a + b)/ab

f(a + b) is not equal to f(a) + f(b)


E. f(x) = -3x

f(a + b) = -3(a + b) = -3a - 3b

f(a) + f(b) = -3a + -3b

f(a + b) is equal to f(a) + f(b) . CORRECT.


choose E.

-BM-

thanks bluementor. i just loved ur explanation. we need not to go for trial n error method by putting various numbers for 2 and 3.