To algebraically determine the inverse of the given relation, we need to exchange x and y and solve for y.
Inverse: f^(- 1)(x)=- 1/4 x Graph:
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Before we can find the inverse of the given function, we need to replace f(x) with y.
f(x)=-4 x ⇔ y=- 4x
To algebraically determine the inverse of the given relation, we exchange x and y and solve for y.
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Given Equation & & Inverse Equation [0.8em]
y=- 4 x & & x=- 4 yThe result of isolating y in the new equation will be the inverse of the given function.
Now, we have the inverse function. Lastly, we need to replace y with f^(- 1)(x).
y=- 1/4x ⇔ f^(- 1)(x)=- 1/4x
Graphing the Function
Because the given function is in slope-intercept form, we can graph it using its slope and y-intercept. It has a slope of - 4 and a y-intercept at (0,0).
Graphing the Inverse of the Function
Because the inverse function is in slope-intercept form, we can graph it using its slope and y-intercept. It has a slope of - 14 and a y-intercept at (0,0).
Let's add it to the graph of the given function so that we can more easily see how it is a reflection across the y=x.
