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Before we can find the inverse of the given function, we need to replace $f(x)$ with $y.$
$f(x)=-2x+5⇔y=-2x+5 $
To algebraically determine the inverse of the given function, we exchange $x$ and $y,$ and solve for $y.$
$y=-2x+5⟶switch x=-2y+5 $
The result of isolating $y$ in the new equation will be the inverse of the given function.
Now, we will replace $y$ with $f_{-1}(x)$ to complete the operation.
$y=25−x ⇔f_{-1}(x)=25−x $ ### Graphing the Function

### Graphing the Inverse of the Function

$x=-2y+5$

$y=25−x $

Because the given function is in slope-intercept form, we can graph it using its slope and $y-$intercept to graph it.

To graph the inverse linear function, let's write it in slope-intercept form. $f_{-1}(x)=25−x ⇔f_{-1}(x)=-21 x+25 $ Now, let's add it to the graph of the given function so that we can more easily see how it is a reflection on the line $y=x.$