To algebraically determine the inverse of the given relation, we need to exchange x and y and solve for y.
Inverse: f^(- 1)(x)=2x+1 Graph:
Practice makes perfect
Before we can find the inverse of the given function, we need to simplify f(x) by rewriting it as a sum of quotients.
f(x)=x-1/2 ⇔ f(x)=x/2-1/2 ⇔ f(x)=1/2x-1/2
Then, we need to replace f(x) with y.
f(x)=1/2x-1/2 ⇔ y=1/2x-1/2To 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=1/2 x-1/2 & & x=1/2 y-1/2
The result of isolating y in the new equation will be the inverse of the given function.
Now we have the inverse of the given function. Lastly, we need to replace y with f^(- 1)(x).
y=2x+1 ⇔ f^(- 1)(x)=2x+1
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 12 and a y-intercept at (0,- 12).
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 2 and a y-intercept at (0,1).
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.
