F(x)=(a*x) - (b*4), f(0)=16, and f(3)=25. what is a+b?

This is a quite interesting problem.

Since it is normally unsolvable without the functions, the answer must lay somewhere in the examples given.

In this case, it lays in f(0).

Why would that be? Because anything times 0 is equal to 0.

In f(0), x is equal to 0, so a*x is therefore equal to 0.

Knowing that, the only thing that is left behind is, when you substitute in 0 for x:

16 = -(b*4)

Therefore, we can then solve to get:

-16 = b * 4

-4 = b

And now it's fairly simple to get a: just plug b into f(3) and solve.

25 = (3a) - (-4*4)

25 = 3a + 16

25 - 16 = 3a

9 = 3a

a = 3

And now to solve for what the question is looking for, just add a and b.

3 + -4 = -1

And there's your answer.

step-by-step explanation: