Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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f−1(x)=198339204x
Evaluate
y=x2×11x×18
Simplify
More Steps

Evaluate
x2×11x×18
Multiply the terms with the same base by adding their exponents
x2+1×11×18
Add the numbers
x3×11×18
Multiply the terms
x3×198
Use the commutative property to reorder the terms
198x3
y=198x3
Interchange x and y
x=198y3
Swap the sides of the equation
198y3=x
Divide both sides
198198y3=198x
Divide the numbers
y3=198x
Take the 3-th root on both sides of the equation
3y3=3198x
Calculate
y=3198x
Simplify the root
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Evaluate
3198x
To take a root of a fraction,take the root of the numerator and denominator separately
31983x
Multiply by the Conjugate
3198×319823x×31982
Calculate
1983x×31982
Calculate
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Evaluate
3x×31982
The product of roots with the same index is equal to the root of the product
3x×1982
Calculate the product
31982x
19831982x
Calculate
198339204x
y=198339204x
Solution
f−1(x)=198339204x
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=x211x18
Simplify the expression
y=198x3
To test if the graph of y=198x3 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=198(−x)3
Simplify
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Evaluate
198(−x)3
Rewrite the expression
198(−x3)
Multiply the numbers
−198x3
−y=−198x3
Change the signs both sides
y=198x3
Solution
Symmetry with respect to the origin
Show Solution

Solve the equation
Solve for x
Solve for y
x=198339204y
Evaluate
y=x2×11x×18
Simplify
More Steps

Evaluate
x2×11x×18
Multiply the terms with the same base by adding their exponents
x2+1×11×18
Add the numbers
x3×11×18
Multiply the terms
x3×198
Use the commutative property to reorder the terms
198x3
y=198x3
Swap the sides of the equation
198x3=y
Divide both sides
198198x3=198y
Divide the numbers
x3=198y
Take the 3-th root on both sides of the equation
3x3=3198y
Calculate
x=3198y
Solution
More Steps

Evaluate
3198y
To take a root of a fraction,take the root of the numerator and denominator separately
31983y
Multiply by the Conjugate
3198×319823y×31982
Calculate
1983y×31982
Calculate
More Steps

Evaluate
3y×31982
The product of roots with the same index is equal to the root of the product
3y×1982
Calculate the product
31982y
19831982y
Calculate
198339204y
x=198339204y
Show Solution

Rewrite the equation
r=0r=198cos3(θ)sin(θ)r=−198cos3(θ)sin(θ)
Evaluate
y=x2×11x×18
Simplify
More Steps

Evaluate
x2×11x×18
Multiply the terms with the same base by adding their exponents
x2+1×11×18
Add the numbers
x3×11×18
Multiply the terms
x3×198
Use the commutative property to reorder the terms
198x3
y=198x3
Move the expression to the left side
y−198x3=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
sin(θ)×r−198(cos(θ)×r)3=0
Factor the expression
−198cos3(θ)×r3+sin(θ)×r=0
Factor the expression
r(−198cos3(θ)×r2+sin(θ))=0
When the product of factors equals 0,at least one factor is 0
r=0−198cos3(θ)×r2+sin(θ)=0
Solution
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Factor the expression
−198cos3(θ)×r2+sin(θ)=0
Subtract the terms
−198cos3(θ)×r2+sin(θ)−sin(θ)=0−sin(θ)
Evaluate
−198cos3(θ)×r2=−sin(θ)
Divide the terms
r2=198cos3(θ)sin(θ)
Evaluate the power
r=±198cos3(θ)sin(θ)
Separate into possible cases
r=198cos3(θ)sin(θ)r=−198cos3(θ)sin(θ)
r=0r=198cos3(θ)sin(θ)r=−198cos3(θ)sin(θ)
Show Solution
