Solving Cubic Composition of Functions

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What is the inverse of f(x) = (x-9)³? Remember that the x and y switch.

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What does it mean to find the inverse of a function?

• The x-values of the original function become the y-values of the inverse and y-values of the original become the x-values of the inverse function.

• The y-values of the original function are the y-values of the inverse function.

• The x's and y's are made negative.

• The x's and y's are the same in the original and inverse functions.

A function and its inverse are shown on the graph. The inverse has been reflected over which line?

• y = x

• y =1

• y = 0

• y = x + 1

What is the inverse of the function

ƒ(x) = 2(4x + 1)³ − 4

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• Square root function

• Quadratic function

• Cubic function

• Exponential Function

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Find the inverse of g(x) = x³ + 2

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  What is the equation for the red function? 

• g(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³

If f(x) = x³ is changed to f(x) = - (x + 3)³ + 2, how is the graph transformed?

• 3 units right, 2 units up, reflected across the y-axis

• 3 units right, 2 units up, reflected across the x-axis

• 3 units left, 2 units up, reflected across the x-axis

• 3 units left, 2 units up, reflected across the y-axis