Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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f−1(x)=30033600x
Evaluate
y=15x3×500
Simplify
y=7500x3
Interchange x and y
x=7500y3
Swap the sides of the equation
7500y3=x
Divide both sides
75007500y3=7500x
Divide the numbers
y3=7500x
Take the 3-th root on both sides of the equation
3y3=37500x
Calculate
y=37500x
Simplify the root
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Evaluate
37500x
To take a root of a fraction,take the root of the numerator and denominator separately
375003x
Simplify the radical expression
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Evaluate
37500
Write the expression as a product where the root of one of the factors can be evaluated
3125×60
Write the number in exponential form with the base of 5
353×60
The root of a product is equal to the product of the roots of each factor
353×360
Reduce the index of the radical and exponent with 3
5360
53603x
Multiply by the Conjugate
5360×36023x×3602
Calculate
5×603x×3602
Calculate
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Evaluate
3x×3602
The product of roots with the same index is equal to the root of the product
3x×602
Calculate the product
3602x
5×603602x
Calculate
3003602x
Calculate
30033600x
y=30033600x
Solution
f−1(x)=30033600x
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=15x3500
Simplify the expression
y=7500x3
To test if the graph of y=7500x3 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=7500(−x)3
Simplify
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Evaluate
7500(−x)3
Rewrite the expression
7500(−x3)
Multiply the numbers
−7500x3
−y=−7500x3
Change the signs both sides
y=7500x3
Solution
Symmetry with respect to the origin
Show Solution

Solve the equation
Solve for x
Solve for y
x=30033600y
Evaluate
y=15x3×500
Simplify
y=7500x3
Swap the sides of the equation
7500x3=y
Divide both sides
75007500x3=7500y
Divide the numbers
x3=7500y
Take the 3-th root on both sides of the equation
3x3=37500y
Calculate
x=37500y
Solution
More Steps

Evaluate
37500y
To take a root of a fraction,take the root of the numerator and denominator separately
375003y
Simplify the radical expression
More Steps

Evaluate
37500
Write the expression as a product where the root of one of the factors can be evaluated
3125×60
Write the number in exponential form with the base of 5
353×60
The root of a product is equal to the product of the roots of each factor
353×360
Reduce the index of the radical and exponent with 3
5360
53603y
Multiply by the Conjugate
5360×36023y×3602
Calculate
5×603y×3602
Calculate
More Steps

Evaluate
3y×3602
The product of roots with the same index is equal to the root of the product
3y×602
Calculate the product
3602y
5×603602y
Calculate
3003602y
Calculate
30033600y
x=30033600y
Show Solution

Rewrite the equation
r=0r=7500cos3(θ)sin(θ)r=−7500cos3(θ)sin(θ)
Evaluate
y=15x3×500
Simplify
y=7500x3
Move the expression to the left side
y−7500x3=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
sin(θ)×r−7500(cos(θ)×r)3=0
Factor the expression
−7500cos3(θ)×r3+sin(θ)×r=0
Factor the expression
r(−7500cos3(θ)×r2+sin(θ))=0
When the product of factors equals 0,at least one factor is 0
r=0−7500cos3(θ)×r2+sin(θ)=0
Solution
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Factor the expression
−7500cos3(θ)×r2+sin(θ)=0
Subtract the terms
−7500cos3(θ)×r2+sin(θ)−sin(θ)=0−sin(θ)
Evaluate
−7500cos3(θ)×r2=−sin(θ)
Divide the terms
r2=7500cos3(θ)sin(θ)
Evaluate the power
r=±7500cos3(θ)sin(θ)
Separate into possible cases
r=7500cos3(θ)sin(θ)r=−7500cos3(θ)sin(θ)
r=0r=7500cos3(θ)sin(θ)r=−7500cos3(θ)sin(θ)
Show Solution
