Name:___________________________________________
Algebra 2 Module 11
Finding the Inverse of a Cubic Function
Graph f (x) = x3
Domain: _______________
Range: _______________
f(x)
f​-1​(x)
Graph the inverse on the same coordinate
plane:
● Switch x and y for each point and re-plot
the points in a new color.
● Draw the line y = x. What do you notice?
● Is the inverse a function? _____ Why or
Why Not?
Domain:____________
Range: _____________
● Solve for the inverse equation, f​-1​(x).
Hint: switch x and y and then solve for y.
f​-1​(x)= __________________ This is the parent
graph of the ​cube root​ function.
The inverse of a cubic graph is the ​cube root​ function.
1. Graph f (x) = − x3
Switch x and y and plot the inverse graph in a
different color. Graph the line y = x.
Solve for the inverse equation:
f​-1​(x)= __________________
f(x)
f​-1​(x)
Domain: __________ Domain: ___________
Range: __________ Range: _____________
f(x)
f​-1​(x)
2. f (x) = x3 + 3
f(x)
f​-1​(x)
Switch x and y and plot the inverse graph in a
different color. Graph the line y = x.
Solve for the inverse equation:
f​-1​(x)= __________________
f(x)
Domain: __________
f​-1​(x)
Domain: __________
Range:
Range: ___________
__________
3. f (x) = (x + 2)3
Switch x and y and plot the inverse graph in a
different color. Graph the line y = x.
f(x)
f​-1​(x)
Solve for the inverse equation:
f​-1​(x)= __________________
f(x)
f​-1​(x)
Domain: __________ Domain: ___________
Range: __________
Range: ____________
4. Solve for the inverse of the given cubic function:
f​-1​(x) = _____________________
f(x) = (x - 3)​3​ - 2