Question

if f(x)= 2^x,
prove that f(a),f(b)= f(a+b)


pls help​

Answer 1

Answer:

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

A. f(x)=x2f(x)=x2

B. f(x)=x+1f(x)=x+1

C. f(x)=x√f(x)=x

D. f(x)=2xf(x)=2x

E. f(x)=−3xf(x)=−3x

A. f(a+b)=(a+b)2=a2+2ab+b2≠f(a)+f(b)=a2+b2f(a+b)=(a+b)2=a2+2ab+b2≠f(a)+f(b)=a2+b2

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

C. f(a+b)=a+b−−−−√≠f(a)+f(b)=a√+b√f(a+b)=a+b≠f(a)+f(b)=a+b.

D. f(a+b)=2a+b≠f(a)+f(b)=2a+2bf(a+b)=2a+b≠f(a)+f(b)=2a+2b.

E. f(a+b)=−3(a+b)=−3a−3b=f(a)+f(b)=−3a−3bf(a+b)=−3(a+b)=−3a−3b=f(a)+f(b)=−3a−3b. Correct.

Step-by-step explanation:

hope u have been understood