Find the linear function f(x) that satisfies both of the following conditions.
(a) f(1) = 3
(b) f(x) = f(x + 1) - 2
The function is linear, thus 2 point shall determine it.
f(1)=3.
Thus, (1,3) is a point on the line.
By condition 2 we have:
f(1) = f(2) -2
Thus,
3=f(2)-2
Thus,
f(2)=5
Hence,
(2,5) is a point on the line.
Now you have two points you can find the equation of the line.