Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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f−1(x)=32x
Evaluate
y=2x2x×1
Simplify
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Evaluate
2x2x×1
Rewrite the expression
2x2x
Multiply the terms
2x2×x
Multiply the terms
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Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
2x3
y=2x3
Interchange x and y
x=2y3
Swap the sides of the equation
2y3=x
Cross multiply
y3=2x
Take the 3-th root on both sides of the equation
3y3=32x
Calculate
y=32x
Solution
f−1(x)=32x
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=2x2x1
Simplify the expression
y=2x3
To test if the graph of y=2x3 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=2(−x)3
Simplify
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Evaluate
2(−x)3
Determine the sign
2−x3
Use b−a=−ba=−ba to rewrite the fraction
−2x3
−y=−2x3
Change the signs both sides
y=2x3
Solution
Symmetry with respect to the origin
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Solve the equation
Solve for x
Solve for y
x=32y
Evaluate
y=2x2x×1
Simplify
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Evaluate
2x2x×1
Rewrite the expression
2x2x
Multiply the terms
2x2×x
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
2x3
y=2x3
Swap the sides of the equation
2x3=y
Cross multiply
x3=2y
Take the 3-th root on both sides of the equation
3x3=32y
Solution
x=32y
Show Solution
Rewrite the equation
r=0r=2sin(θ)sec(θ)×∣sec(θ)∣r=−2sin(θ)sec(θ)×∣sec(θ)∣
Evaluate
y=2x2x×1
Simplify
More Steps
Evaluate
2x2x×1
Rewrite the expression
2x2x
Multiply the terms
2x2×x
Multiply the terms
More Steps
Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
2x3
y=2x3
Multiply both sides of the equation by LCD
y×2=2x3×2
Use the commutative property to reorder the terms
2y=2x3×2
Simplify the equation
2y=x3
Move the expression to the left side
2y−x3=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
2sin(θ)×r−(cos(θ)×r)3=0
Factor the expression
−cos3(θ)×r3+2sin(θ)×r=0
Factor the expression
r(−cos3(θ)×r2+2sin(θ))=0
When the product of factors equals 0,at least one factor is 0
r=0−cos3(θ)×r2+2sin(θ)=0
Solution
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Factor the expression
−cos3(θ)×r2+2sin(θ)=0
Subtract the terms
−cos3(θ)×r2+2sin(θ)−2sin(θ)=0−2sin(θ)
Evaluate
−cos3(θ)×r2=−2sin(θ)
Divide the terms
r2=cos3(θ)2sin(θ)
Simplify the expression
r2=2sin(θ)sec3(θ)
Evaluate the power
r=±2sin(θ)sec3(θ)
Simplify the expression
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Evaluate
2sin(θ)sec3(θ)
Rewrite the exponent as a sum
2sin(θ)sec2+1(θ)
Use am+n=am×an to expand the expression
2sin(θ)sec2(θ)sec(θ)
Rewrite the expression
sec2(θ)×2sin(θ)sec(θ)
Calculate
∣sec(θ)∣×2sin(θ)sec(θ)
Calculate
2sin(θ)sec(θ)×∣sec(θ)∣
r=±(2sin(θ)sec(θ)×∣sec(θ)∣)
Separate into possible cases
r=2sin(θ)sec(θ)×∣sec(θ)∣r=−2sin(θ)sec(θ)×∣sec(θ)∣
r=0r=2sin(θ)sec(θ)×∣sec(θ)∣r=−2sin(θ)sec(θ)×∣sec(θ)∣
Show Solution
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