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Question
y=-x^{2}\times 7x
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) = -\frac{\sqrt[3]{49x}}{7}
Evaluate
y=-x^{2}\times 7x
Simplify
More Steps
Evaluate
-x^{2}\times 7x
Multiply
More Steps
Evaluate
x^{2}\times 7x
Multiply the terms with the same base by adding their exponents
x^{2+1}\times 7
Add the numbers
x^{3}\times 7
Use the commutative property to reorder the terms
7x^{3}
-7x^{3}
y=-7x^{3}
\text{Interchange }x\text{ and }y
x=-7y^{3}
Swap the sides of the equation
-7y^{3}=x
Change the signs on both sides of the equation
7y^{3}=-x
Divide both sides
\frac{7y^{3}}{7}=\frac{-x}{7}
Divide the numbers
y^{3}=\frac{-x}{7}
\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}
y^{3}=-\frac{x}{7}
\text{Take the }3\text{-th root on both sides of the equation}
\sqrt[3]{y^{3}}=\sqrt[3]{-\frac{x}{7}}
Calculate
y=\sqrt[3]{-\frac{x}{7}}
Simplify the root
More Steps
Evaluate
\sqrt[3]{-\frac{x}{7}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[3]{-x}}{\sqrt[3]{7}}
Multiply by the Conjugate
\frac{\sqrt[3]{-x}\times \sqrt[3]{7^{2}}}{\sqrt[3]{7}\times \sqrt[3]{7^{2}}}
Calculate
\frac{\sqrt[3]{-x}\times \sqrt[3]{7^{2}}}{7}
Calculate
More Steps
Evaluate
\sqrt[3]{-x}\times \sqrt[3]{7^{2}}
The product of roots with the same index is equal to the root of the product
\sqrt[3]{-x\times 7^{2}}
Calculate the product
\sqrt[3]{-7^{2}x}
An odd root of a negative radicand is always a negative
-\sqrt[3]{7^{2}x}
\frac{-\sqrt[3]{7^{2}x}}{7}
Calculate
-\frac{\sqrt[3]{7^{2}x}}{7}
Calculate
-\frac{\sqrt[3]{49x}}{7}
y=-\frac{\sqrt[3]{49x}}{7}
Solution
f^{-1}\left(x\right) = -\frac{\sqrt[3]{49x}}{7}
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
y=-x^{2}7x
Simplify the expression
y=-7x^{3}
\text{To test if the graph of }y=-7x^{3}\text{ is symmetry with respect to the origin,substitute -x for x and -y for y}
-y=-7\left(-x\right)^{3}
Simplify
More Steps
Evaluate
-7\left(-x\right)^{3}
Rewrite the expression
-7\left(-x^{3}\right)
Multiply the numbers
7x^{3}
-y=7x^{3}
Change the signs both sides
y=-7x^{3}
Solution
\textrm{Symmetry with respect to the origin}
Show Solutions
Solve the equation
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\text{Solve for }x
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\text{Solve for }y
x=-\frac{\sqrt[3]{49y}}{7}
Evaluate
y=-x^{2}\times 7x
Simplify
More Steps
Evaluate
-x^{2}\times 7x
Multiply
More Steps
Evaluate
x^{2}\times 7x
Multiply the terms with the same base by adding their exponents
x^{2+1}\times 7
Add the numbers
x^{3}\times 7
Use the commutative property to reorder the terms
7x^{3}
-7x^{3}
y=-7x^{3}
Swap the sides of the equation
-7x^{3}=y
Change the signs on both sides of the equation
7x^{3}=-y
Divide both sides
\frac{7x^{3}}{7}=\frac{-y}{7}
Divide the numbers
x^{3}=\frac{-y}{7}
\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}
x^{3}=-\frac{y}{7}
\text{Take the }3\text{-th root on both sides of the equation}
\sqrt[3]{x^{3}}=\sqrt[3]{-\frac{y}{7}}
Calculate
x=\sqrt[3]{-\frac{y}{7}}
Solution
More Steps
Evaluate
\sqrt[3]{-\frac{y}{7}}
To take a root of a fraction,take the root of the numerator and denominator separately
\frac{\sqrt[3]{-y}}{\sqrt[3]{7}}
Multiply by the Conjugate
\frac{\sqrt[3]{-y}\times \sqrt[3]{7^{2}}}{\sqrt[3]{7}\times \sqrt[3]{7^{2}}}
Calculate
\frac{\sqrt[3]{-y}\times \sqrt[3]{7^{2}}}{7}
Calculate
More Steps
Evaluate
\sqrt[3]{-y}\times \sqrt[3]{7^{2}}
The product of roots with the same index is equal to the root of the product
\sqrt[3]{-y\times 7^{2}}
Calculate the product
\sqrt[3]{-7^{2}y}
An odd root of a negative radicand is always a negative
-\sqrt[3]{7^{2}y}
\frac{-\sqrt[3]{7^{2}y}}{7}
Calculate
-\frac{\sqrt[3]{7^{2}y}}{7}
Calculate
-\frac{\sqrt[3]{49y}}{7}
x=-\frac{\sqrt[3]{49y}}{7}
Show Solutions
Rewrite the equation
\begin{align}&r=0\\&r=\sqrt{-\frac{\sin\left(\theta \right)}{7\cos^{3}\left(\theta \right)}}\\&r=-\sqrt{-\frac{\sin\left(\theta \right)}{7\cos^{3}\left(\theta \right)}}\end{align}
Evaluate
y=-x^{2}\times 7x
Simplify
More Steps
Evaluate
-x^{2}\times 7x
Multiply
More Steps
Evaluate
x^{2}\times 7x
Multiply the terms with the same base by adding their exponents
x^{2+1}\times 7
Add the numbers
x^{3}\times 7
Use the commutative property to reorder the terms
7x^{3}
-7x^{3}
y=-7x^{3}
Move the expression to the left side
y+7x^{3}=0
\text{To convert the equation to polar coordinates,substitute }r\cos\left(\theta \right)\text{ for }x\text{ and }r\sin\left(\theta \right)\text{ for }y
\sin\left(\theta \right)\times r+7\left(\cos\left(\theta \right)\times r\right)^{3}=0
Factor the expression
7\cos^{3}\left(\theta \right)\times r^{3}+\sin\left(\theta \right)\times r=0
Factor the expression
r\left(7\cos^{3}\left(\theta \right)\times r^{2}+\sin\left(\theta \right)\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&r=0\\&7\cos^{3}\left(\theta \right)\times r^{2}+\sin\left(\theta \right)=0\end{align}
Solution
More Steps
Factor the expression
7\cos^{3}\left(\theta \right)\times r^{2}+\sin\left(\theta \right)=0
Subtract the terms
7\cos^{3}\left(\theta \right)\times r^{2}+\sin\left(\theta \right)-\sin\left(\theta \right)=0-\sin\left(\theta \right)
Evaluate
7\cos^{3}\left(\theta \right)\times r^{2}=-\sin\left(\theta \right)
Divide the terms
r^{2}=-\frac{\sin\left(\theta \right)}{7\cos^{3}\left(\theta \right)}
Evaluate the power
r=\pm \sqrt{-\frac{\sin\left(\theta \right)}{7\cos^{3}\left(\theta \right)}}
Separate into possible cases
\begin{align}&r=\sqrt{-\frac{\sin\left(\theta \right)}{7\cos^{3}\left(\theta \right)}}\\&r=-\sqrt{-\frac{\sin\left(\theta \right)}{7\cos^{3}\left(\theta \right)}}\end{align}
\begin{align}&r=0\\&r=\sqrt{-\frac{\sin\left(\theta \right)}{7\cos^{3}\left(\theta \right)}}\\&r=-\sqrt{-\frac{\sin\left(\theta \right)}{7\cos^{3}\left(\theta \right)}}\end{align}
Show Solutions
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