Can someone help me with this problem?

Question

"Find a linear function (6) that satisfies both of the given conditions"

1. f (-1) = 1 + f (2) , f (3) = 4 f (1)

Can anyone show me the steps to working out this problem please

thanks for your answers

Answer 1

Well, you have been told that the function is linear, therefore:
f(x) = ax + b, where a and b is to be determined.
Since: f (-1) = 1 + f (2)
we have: -a + b = 1 + 2a + b
Hence a = - 1/3, lead to:
f(x) = - x/3 + b
Since: f (3) = 4 f (1)
we have: -1 + b = 4(-1/3 + b)
Hence b = 1/9, and finally we have:
f(x) = - x/3 + 1/9