SOLUTION: Determine if the statement is true or false. If statement is false, make the necessary change(s) to produce a true statement. If f (x) = 2^x then f(a+b)= f(a)+f(b)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Determine if the statement is true or false. If statement is false, make the necessary change(s) to produce a true statement. If f (x) = 2^x then f(a+b)= f(a)+f(b)      Log On


   

Question 1188809: Determine if the statement is true or false. If statement is false, make the necessary change(s) to produce a true statement.
If f (x) = 2^x then f(a+b)= f(a)+f(b)
Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Determine if the statement is true or false. If statement is false, make the necessary change(s) to produce a true statement.
If f (x) = 2^x then f(a+b)= f(a)+f(b)
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f(a) = 2^a
f(b) = 2^b
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f(a+b) = 2^a + 2^b
==================
Sub a+b for x:
f(a+b) = 2^(a+b)
Therefore, it is false.

Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.

The statement is FALSE.


To check that it is false, calculate  f(a+b)  and  f(a) + f(b)  at these values a= 1, b= 2.


The correct statement is  


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


Check it on your own.