SOLUTION: Evaluate the function at the given value of the independent variable and simplify. f(x) = 3x-1 f(x)-f(1) _________ x-1 I started working this problem but I think I'm doi

Algebra ->  Rational-functions -> SOLUTION: Evaluate the function at the given value of the independent variable and simplify. f(x) = 3x-1 f(x)-f(1) _________ x-1 I started working this problem but I think I'm doi      Log On


   

Question 236145: Evaluate the function at the given value of the independent variable and simplify. f(x) = 3x-1
f(x)-f(1)
_________
x-1
I started working this problem but I think I'm doing it the wrong way. I'm not sure if I'm suppose to substitue the 3x-1 in each place of f or x?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your equation is f(x) = (3x-1)

They want you to evaluate %28f%28x%29-f%281%29%29%2F%28x-1%29

If so, this is how you do it.

Let g(x) = %28f%28x%29-f%281%29%29%2F%28x-1%29

You replace f(x) with (3x-1) because that's what f(x) is equal to.

You replace x with 1 in f(x) = 3x-1 to get f(1) = 3*1-1 = 2

You are left with:

g(x) = %28f%28x%29-f%281%29%29%2F%28x-1%29 = %28%283x-1%29+-+2%29%2F%28x-1%29

This becomes:

g(x) = %283x-3%29%2F%28x-1%29

You can factor the numerator to get

g(x) = %283x-3%29%2F%28x-1%29 = %283%2A%28x-1%29%29%2F%28x-1%29

This becomes:

g(x) = 3