To find the inverse of the function [tex]\( f(x) = \frac{1}{3} x + 2 \)[/tex], follow these steps:
1. Set [tex]\( y = f(x) \)[/tex]:
[tex]\[
y = \frac{1}{3} x + 2
\][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[
x = \frac{1}{3} y + 2
\][/tex]
3. Solve for [tex]\( y \)[/tex]:
[tex]\[
x = \frac{1}{3} y + 2
\][/tex]
Multiply both sides by 3 to clear the fraction:
[tex]\[
3x = y + 6
\][/tex]
Subtract 6 from both sides to isolate [tex]\( y \)[/tex]:
[tex]\[
y = 3x - 6
\][/tex]
4. Thus, the inverse function is:
[tex]\[
h(x) = 3x - 6
\][/tex]
So, the correct inverse function is [tex]\( h(x) = 3x - 6 \)[/tex].
