Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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f−1(x)=−6333969x
Evaluate
y=−3x2×3x×7
Simplify
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Evaluate
−3x2×3x×7
Multiply the terms
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Evaluate
3×3×7
Multiply the terms
9×7
Multiply the numbers
63
−63x2×x
Multiply the terms with the same base by adding their exponents
−63x2+1
Add the numbers
−63x3
y=−63x3
Interchange x and y
x=−63y3
Swap the sides of the equation
−63y3=x
Change the signs on both sides of the equation
63y3=−x
Divide both sides
6363y3=63−x
Divide the numbers
y3=63−x
Use b−a=−ba=−ba to rewrite the fraction
y3=−63x
Take the 3-th root on both sides of the equation
3y3=3−63x
Calculate
y=3−63x
Simplify the root
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Evaluate
3−63x
To take a root of a fraction,take the root of the numerator and denominator separately
3633−x
Multiply by the Conjugate
363×36323−x×3632
Calculate
633−x×3632
Calculate
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Evaluate
3−x×3632
The product of roots with the same index is equal to the root of the product
3−x×632
Calculate the product
3−632x
An odd root of a negative radicand is always a negative
−3632x
63−3632x
Calculate
−633632x
Calculate
−6333969x
y=−6333969x
Solution
f−1(x)=−6333969x
Show Solution

Testing for symmetry
Testing for symmetry about the origin
Testing for symmetry about the x-axis
Testing for symmetry about the y-axis
Symmetry with respect to the origin
Evaluate
y=−3x23x7
Simplify the expression
y=−63x3
To test if the graph of y=−63x3 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=−63(−x)3
Simplify
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Evaluate
−63(−x)3
Rewrite the expression
−63(−x3)
Multiply the numbers
63x3
−y=63x3
Change the signs both sides
y=−63x3
Solution
Symmetry with respect to the origin
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Solve the equation
Solve for x
Solve for y
x=−6333969y
Evaluate
y=−3x2×3x×7
Simplify
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Evaluate
−3x2×3x×7
Multiply the terms
More Steps

Evaluate
3×3×7
Multiply the terms
9×7
Multiply the numbers
63
−63x2×x
Multiply the terms with the same base by adding their exponents
−63x2+1
Add the numbers
−63x3
y=−63x3
Swap the sides of the equation
−63x3=y
Change the signs on both sides of the equation
63x3=−y
Divide both sides
6363x3=63−y
Divide the numbers
x3=63−y
Use b−a=−ba=−ba to rewrite the fraction
x3=−63y
Take the 3-th root on both sides of the equation
3x3=3−63y
Calculate
x=3−63y
Solution
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Evaluate
3−63y
To take a root of a fraction,take the root of the numerator and denominator separately
3633−y
Multiply by the Conjugate
363×36323−y×3632
Calculate
633−y×3632
Calculate
More Steps

Evaluate
3−y×3632
The product of roots with the same index is equal to the root of the product
3−y×632
Calculate the product
3−632y
An odd root of a negative radicand is always a negative
−3632y
63−3632y
Calculate
−633632y
Calculate
−6333969y
x=−6333969y
Show Solution

Rewrite the equation
r=0r=−63cos3(θ)sin(θ)r=−−63cos3(θ)sin(θ)
Evaluate
y=−3x2×3x×7
Simplify
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Evaluate
−3x2×3x×7
Multiply the terms
More Steps

Evaluate
3×3×7
Multiply the terms
9×7
Multiply the numbers
63
−63x2×x
Multiply the terms with the same base by adding their exponents
−63x2+1
Add the numbers
−63x3
y=−63x3
Move the expression to the left side
y+63x3=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
sin(θ)×r+63(cos(θ)×r)3=0
Factor the expression
63cos3(θ)×r3+sin(θ)×r=0
Factor the expression
r(63cos3(θ)×r2+sin(θ))=0
When the product of factors equals 0,at least one factor is 0
r=063cos3(θ)×r2+sin(θ)=0
Solution
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Factor the expression
63cos3(θ)×r2+sin(θ)=0
Subtract the terms
63cos3(θ)×r2+sin(θ)−sin(θ)=0−sin(θ)
Evaluate
63cos3(θ)×r2=−sin(θ)
Divide the terms
r2=−63cos3(θ)sin(θ)
Evaluate the power
r=±−63cos3(θ)sin(θ)
Separate into possible cases
r=−63cos3(θ)sin(θ)r=−−63cos3(θ)sin(θ)
r=0r=−63cos3(θ)sin(θ)r=−−63cos3(θ)sin(θ)
Show Solution
