Question

True or false. If f is a function, the f(s+t) = f(s)+f(t). ...?

Answer 1

The statement is true for linear functions, but not in general for all functions.

Step-by-step explanation:

The statement is true if f(x) is a linear function.

However, it is not true in general for all functions, so the statement is false.

An example of a linear function where the statement is true would be f(x) = 2x.

If we substitute s + t into the function, we get f(s + t) = 2(s + t) = 2s + 2t.

On the other hand, if we substitute f(s) + f(t) into the function, we get f(s) + f(t) = 2s + 2t.

Therefore, the equality holds and the statement is true for linear functions.

Answer 2

Can be true or false.

True:
f(x)=x
f(3+5)=3+5=8
f(3+5)=f(3)+f(5)=3+5=8

False:

`f(x)=x^2 \\f(3+5)=(3+5)^2=8^2=64 \\f(3+5)=f(3)+f(5)=3^2+5^2=9+25=34`