linear function

Question

Find the parameters a and b included in the linear function f(x) = a x + b so that f -1 (2) = 3 and f -1 (-3) = 6, where f -1 (x) is the inverse of function f.

Answer 1

Since f^-1(2) = 3, f(3) = 2 and since f^-1(-3) = 6, f(6) = -3.

So, f(3) = 3a + b = 2 and f(6) = 6a + b = -3.

3a + b = 2

6a + b = -3

Subtract the equations to get -3a = 5.

Therefore, a = -5/3 and b = 7.

So, f(x) = (-5/3)x + 7.