Question

Simplify f(x) = (3x^2-4x+1)/(3x-1). Using complete sentences, explain why f(1) = 0, f(0) = -1, and f(-1) = -2, yet f(1/3) is undefined.

please show how u do it so i can understand

Answer 1

Can you factor the top?

Answer 2

Factor numerator 3 x^2 - 4x + 1 = (-3 x + 1) (-1 x + 1)
f(x) = (3 x -1) (x - 1)/(3 x -1)
f(1) =0
f(0)=-1
f(1/3)=0/0 ?
With Calculus L'Hospital rule
f(1/3)=(6( (1/3) - 4)/3 = -2/3
this is a continuous function

Answer 3

L'Hosptal Rule
f(x) = N(x)/D(x)
f(x1) = 0/0 or infinity/infinity
f(x1) = N'(x1)/D'(x1)
in the above problem 3x -1 do cancel out