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Question
f\left(x\right)=x^{3}
Function
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Find the inverse
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Evaluate the derivative
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Find the domain
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\text{Find the }x\text{-intercept/zero}
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Find the y-intercept
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Find the critical numbers
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Find the local extrema
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Find the increasing or decreasing interval
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Find the range
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Find the vertical asymptotes
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Find the horizontal asymptotes
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Find the oblique asymptotes
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Determine if even, odd or neither
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Find the stationary points
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Find the inflection points
More methods
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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}
Show Solutions
Testing for symmetry
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Testing for symmetry about the origin
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Testing for symmetry about the x-axis
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Testing for symmetry about the y-axis
\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}
Show Solutions
Graph
