Introduction to Cube Roots

Inverse of Cubes and Cube Roots

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Inverses in Graphs

• The cube root and cubic functions are inverse of each other

• They reflect over the line y=x

• The domain and range of each function are also switched

Multiple Choice

Find the inverse of y = (x+2)³ + 7

• y = ∛(x-7)-2

• y = ∛(x-2) -7

• y = (x - 7)³ -2

• y = (x-2)³ - 7

Multiple Choice

Find the inverse of y = x³ + 7

• y = ∛(x-7)

• y = ∛x -7

• y = (x - 7)³

• y = x³ - 7

Multiple Choice

Which is f^-1(x)?

• f^-1(x)=4+∛(x+5)

• f^-1(x)=∛(x+4) +5

• f^-1(x)=5+(x+4)³

• f^-1(x)=4+(x+5)³

Multiple Choice

Find the inverse: f(x) = x³-1

• f^-1(x)= ³√x+1

• f^-1(x)= ³√x-1

• f^-1(x)= (x-1)/3

• f^-1(x)= (x+1)/3

Multiple Choice

Which is f^-1(x)?

• f^-1(x)=(x/5)³
• f^-1(x)=1/5(x)³
• f^-1(x)=5(x)³
• f^-1(x)=125(x)³

Multiple Choice

Which is f^-1(x)?

• f^-1(x)=∛(x-8) + 6

• f^-1(x)=∛(x+6) - 8

• f^-1(x)=(x+6)³ - 8

• f^-1(x)=(x-8)³ + 6

Multiple Choice

Which is f^-1(x)?

• f^-1(x)=4(x+3)³

• f^-1(x)=(4x+12)³

• f^-1(x)=3+1/4(x)³

• f^-1(x)=1/4(x+3)³

Multiple Choice

What is the inverse of the function?

• $$f^{-1}\left(x\right)=\ \left(\frac{x-9}{3}\right)^3$$

• $$f^{-1}\left(x\right)=\ \left(\frac{x-3}{9}\right)^3$$

• $$f^{-1}\left(x\right)=^3\sqrt{\frac{x-9}{3}}$$

• $$f^{-1}\left(x\right)=^3\sqrt{x-9}+3$$