To solve the problem step-by-step, let's break down the expressions given and compute the result:
1. Define the function [tex]\( f(x) \)[/tex]:
[tex]\[
f(x) = 3x - 1
\][/tex]
2. Evaluate [tex]\( f(1) \)[/tex]:
[tex]\[
f(1) = 3(1) - 1 = 2
\][/tex]
3. Set up the expression to compute:
[tex]\[
\frac{f(x) - f(1)}{x - 1}
\][/tex]
We already know from step 2 that [tex]\( f(1) = 2 \)[/tex]. Therefore, the expression becomes:
[tex]\[
\frac{f(x) - 2}{x - 1}
\][/tex]
4. Substitute the function [tex]\( f(x) = 3x - 1 \)[/tex] into the expression:
[tex]\[
\frac{(3x - 1) - 2}{x - 1}
\][/tex]
5. Simplify the numerator:
[tex]\[
(3x - 1) - 2 = 3x - 3
\][/tex]
So the expression now is:
[tex]\[
\frac{3x - 3}{x - 1}
\][/tex]
6. Factor out the common term in the numerator:
[tex]\[
\frac{3(x - 1)}{x - 1}
\][/tex]
7. Cancel the common factor (assuming [tex]\( x \neq 1 \)[/tex]):
[tex]\[
\frac{3(x - 1)}{x - 1} = 3
\][/tex]
Thus, our final answer simplifies to 3. To confirm our findings, [tex]\( f(1) \)[/tex] was computed as 2, and the expression simplifies to 3.
So in summary:
- The value of [tex]\( f(1) \)[/tex] is [tex]\( 2 \)[/tex].
- The given expression simplifies to [tex]\( 3 \)[/tex].
