If f(2)= -2, f-1(6)=10 and f-1(1)=0, what is the function?

Answer 1

f(2) = -2

f(10) = 6

f(0) = 1

we are given 3 data points so it is at most quadratic

Ax^2 + Bx + C = f(x)

f(0)= 1 ---> C = 1

Ax^2 + Bx + 1 = f(x)

f(2) = -2

4A + 2B + 1 = -2

4A + 2B = -3

100A + 10B + 1 = 6

100A + 10B = 5

Solves the 2 by 2 via elimination:

4A + 2B = -3

100A + 10B = 5

-25 * top + bottom:

-40B = 80

B = -2

4A + 2( -2) = -3

4A - 4 = -3

4A = 1

A = 1/4

(1/4)x^2 - 2x + 1 = f(x)