To evaluate [tex]\( f^{-1}(1) \)[/tex] for the function [tex]\( f(x) = 3x - 2 \)[/tex], we aim to find the value of [tex]\( x \)[/tex] such that [tex]\( f(x) = 1 \)[/tex]. Follow these steps:
1. Set up the equation: Start by setting the function equal to 1.
[tex]\[
f(x) = 1
\][/tex]
Given [tex]\( f(x) = 3x - 2 \)[/tex], we substitute [tex]\( f(x) \)[/tex] with [tex]\( 3x - 2 \)[/tex]:
[tex]\[
3x - 2 = 1
\][/tex]
2. Solve for [tex]\( x \)[/tex]:
To isolate [tex]\( x \)[/tex], first add 2 to both sides of the equation:
[tex]\[
3x - 2 + 2 = 1 + 2
\][/tex]
This simplifies to:
[tex]\[
3x = 3
\][/tex]
3. Divide by 3: To find [tex]\( x \)[/tex], divide both sides of the equation by 3:
[tex]\[
x = \frac{3}{3}
\][/tex]
Simplifying the fraction, we find:
[tex]\[
x = 1
\][/tex]
4. Conclusion: The value of [tex]\( x \)[/tex] that satisfies [tex]\( f(x) = 1 \)[/tex] is [tex]\( x = 1 \)[/tex].
Therefore, [tex]\( f^{-1}(1) = 1 \)[/tex].
