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f(x)=x^3

Algebra Calculus Trigonometry Matrix

Question

f\left(x\right)=x^{3}

Function

f^{-1}\left(x\right) = \sqrt[3]{x}

Evaluate

f\left(x\right)=x^{3}

\text{In the equation for }f\left(x\right)\text{,replace }f\left(x\right)\text{ with }y

y=x^{3}

\text{Interchange }x\text{ and }y

x=y^{3}

Swap the sides of the equation

y^{3}=x

\text{Take the }3\text{-th root on both sides of the equation}

\sqrt[3]{y^{3}}=\sqrt[3]{x}

Calculate

y=\sqrt[3]{x}

Solution

f^{-1}\left(x\right) = \sqrt[3]{x}

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Find the inverse

Evaluate the derivative

Find the domain

\text{Find the }x\text{-intercept/zero}

Find the y-intercept

Find the critical numbers

Find the local extrema

Find the increasing or decreasing interval

Find the range

Find the vertical asymptotes

Find the horizontal asymptotes

Find the oblique asymptotes

Determine if even, odd or neither

Find the stationary points

Find the inflection points

Testing for symmetry

\textrm{Symmetry with respect to the origin}

Evaluate

f\left(x\right)=x^{3}

Rewrite the function using the appropriate notation

y=x^{3}

\text{To test if the graph of }y=x^{3}\text{ is symmetry with respect to the origin,substitute -x for x and -y for y}

-y=\left(-x\right)^{3}

Simplify

-y=-x^{3}

Change the signs both sides

y=x^{3}

Solution

\textrm{Symmetry with respect to the origin}

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Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Graph

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