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

Hello there!

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.

a + b = - 1