Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the inverse
Evaluate the derivative
Find the domain
Load more
f−1(x)=−33x
Evaluate
y=−31x3
Interchange x and y
x=−31y3
Swap the sides of the equation
−31y3=x
Change the signs on both sides of the equation
31y3=−x
Multiply by the reciprocal
31y3×3=−x×3
Multiply
y3=−x×3
Use the commutative property to reorder the terms
y3=−3x
Take the 3-th root on both sides of the equation
3y3=3−3x
Calculate
y=3−3x
Simplify the root
More Steps
Evaluate
3−3x
Rewrite the expression
3−3×3x
Simplify the root
−33x
y=−33x
Solution
f−1(x)=−33x
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=−31x3
To test if the graph of y=−31x3 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=−31(−x)3
Simplify
More Steps
Evaluate
−31(−x)3
Rewrite the expression
−31(−x3)
Multiplying or dividing an even number of negative terms equals a positive
31x3
−y=31x3
Change the signs both sides
y=−31x3
Solution
Symmetry with respect to the origin
Show Solution
Solve the equation
x=−33y
Evaluate
y=−31x3
Swap the sides of the equation
−31x3=y
Change the signs on both sides of the equation
31x3=−y
Multiply by the reciprocal
31x3×3=−y×3
Multiply
x3=−y×3
Use the commutative property to reorder the terms
x3=−3y
Take the 3-th root on both sides of the equation
3x3=3−3y
Calculate
x=3−3y
Solution
More Steps
Evaluate
3−3y
Rewrite the expression
3−3×3y
Simplify the root
−33y
x=−33y
Show Solution
Rewrite the equation
r=0r=−3sin(θ)sec(θ)×∣sec(θ)∣r=−−3sin(θ)sec(θ)×∣sec(θ)∣
Evaluate
y=−31x3
Multiply both sides of the equation by LCD
y×3=−31x3×3
Use the commutative property to reorder the terms
3y=−31x3×3
Simplify the equation
3y=−x3
Move the expression to the left side
3y+x3=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
3sin(θ)×r+(cos(θ)×r)3=0
Factor the expression
cos3(θ)×r3+3sin(θ)×r=0
Factor the expression
r(cos3(θ)×r2+3sin(θ))=0
When the product of factors equals 0,at least one factor is 0
r=0cos3(θ)×r2+3sin(θ)=0
Solution
More Steps
Factor the expression
cos3(θ)×r2+3sin(θ)=0
Subtract the terms
cos3(θ)×r2+3sin(θ)−3sin(θ)=0−3sin(θ)
Evaluate
cos3(θ)×r2=−3sin(θ)
Divide the terms
r2=−cos3(θ)3sin(θ)
Simplify the expression
r2=−3sin(θ)sec3(θ)
Evaluate the power
r=±−3sin(θ)sec3(θ)
Simplify the expression
More Steps
Evaluate
−3sin(θ)sec3(θ)
Rewrite the exponent as a sum
−3sin(θ)sec2+1(θ)
Use am+n=am×an to expand the expression
−3sin(θ)sec2(θ)sec(θ)
Rewrite the expression
sec2(θ)(−3sin(θ)sec(θ))
Calculate
∣sec(θ)∣×−3sin(θ)sec(θ)
Calculate
−3sin(θ)sec(θ)×∣sec(θ)∣
r=±(−3sin(θ)sec(θ)×∣sec(θ)∣)
Separate into possible cases
r=−3sin(θ)sec(θ)×∣sec(θ)∣r=−−3sin(θ)sec(θ)×∣sec(θ)∣
r=0r=−3sin(θ)sec(θ)×∣sec(θ)∣r=−−3sin(θ)sec(θ)×∣sec(θ)∣
Show Solution
Graph
