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

(3x^2-4x+1)/(3x-1).


lets try to factor numerator

(3x 1)(x 1)

to negative will work

(3x-1)(x-1)

Answer 2

(3x-1)(x-1)
--------------
3x-1

simplifies to

(x-1)

Answer 3

To see why
f(1) = 0, f(0) = -1, and f(-1) = -2
just plug in the numbers into the function
i.e.
\[f(x)=\frac{3x^2-4x+1}{3x-1}\]with x=1 becomes\[f(1)=\frac{3(1)^2-4(1)+1}{3(1)-1}=\frac{0}{2}=0\]do the same with x=0 and x=-1 and you will get the expected value for f(x) Now try it for f(1/3):\[f(1/3)=\frac{3(1/3)^2-4(1/3)+1}{3(1/3)-1}=\frac{0}{0}\]which is undefined, because anything divided by 0 is undefined.

Answer 4

The denominator is where to look to find where a function is undefined.

Note that imranmeah's factorization of the function is not valid at the point x=1/3, so even though it can be simplified for practical purposes, you must always consult the original function to see where it may be undefined.

Answer 5

thank you so much. I think I actually understand how to do it now.