Question

listen
find the inverse of $f(x)=\frac{1}{3}x - 2$.
the inverse is $g(x)=\square$.
graph the function and its inverse.
line
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Explanation:

Step1: Replace $f(x)$ with $y$

$y = \frac{1}{3}x - 2$

Step2: Swap $x$ and $y$

$x = \frac{1}{3}y - 2$

Step3: Solve for $y$, isolate term with $y$

$x + 2 = \frac{1}{3}y$

Step4: Multiply by 3 to solve for $y$

$y = 3(x + 2) = 3x + 6$

Answer:

$g(x)=3x+6$

Graphing Notes (for reference):

1. For $f(x)=\frac{1}{3}x-2$: Plot the y-intercept $(0, -2)$, then use slope $\frac{1}{3}$ (rise 1, run 3) to find another point like $(3, -1)$, then draw the line.
2. For $g(x)=3x+6$: Plot the y-intercept $(0, 6)$, then use slope $3$ (rise 3, run 1) to find another point like $(1, 9)$, then draw the line. The two lines will be symmetric across the line $y=x$.