What is the linear function f if f(1-x)=3x+2?

We'll recall the standard form of a linear
function:

f(x) = ax + b

Since
we know the determined form of f(1-x), we'll replace x by (1-x) in the standard form of
linear function.

f(1-x) = a(1-x) +
b

We'll remove the
brackets:

f(1-x) = a - ax +
b

But f(1-x) = 3x +
2

Comparing, we'll get:

a - ax
+ b = 3x + 2

-a = 3 => a =
-3

a + b = 2 => -3 + b = 2 => b = 2 + 3
=> b = 5

The required linear function
is: f(x) = -3x + 5.