For given functions A..E we need one which is such that

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

A. f(x) = x^2 i.e. f(a+b) = (a+b)^2

This is not equal to a^2 + b^2 = f(a) + f(b)

B. f(x) = x+1

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

f(a) + f(b) = a+1 + b+1 = a+b+2 which is not eq. f(a+b)

C. f(x) = sqrt(x)

f(a+b) = sqrt(a+b) which is not eq. sqrt(a) + sqrt(b)

D. f(x) = 2/x

f(a+b) = 2/(a+b) which is not eq to 2/a + 2/b

E. f(x) = -3x

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

Therefore E.

MA wrote:

guys, i am dumb on this one. i like to know every step on this one.

thankx..