if g(x) is an antiderivative for f(x) and g(2)=-7 then g(4)=

Question

I confused on if I'm suppose to use the indefinte integral 2 to 4

Answer 1

There seems to be insufficient information because f(x) hasn’t been defined.

For example, if g(x)=x²-11, then f(x)=2x, and g(2)=4-11=-7, so g(4)=16-11=5.

But, if g(x)=1-x³, then f(x)=-3x², and g(2)=-7, so g(4)=1-64=-63. Note that f(x) is redundant because it’s not involved in determining g(4).

And many more examples could be cited, so there is no unique answer.