Algebra
Calculus
Trigonometry
Matrix
Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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f−1(x)=2548x
Evaluate
y=32x5
Interchange x and y
x=32y5
Swap the sides of the equation
32y5=x
Multiply by the reciprocal
32y5×23=x×23
Multiply
y5=x×23
Multiply
y5=23x
Take the 5-th root on both sides of the equation
5y5=523x
Calculate
y=523x
Simplify the root
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Evaluate
523x
Rewrite the expression
523×5x
Simplify the root
2548x
y=2548x
Solution
f−1(x)=2548x
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=32x5
To test if the graph of y=32x5 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=32(−x)5
Simplify
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Evaluate
32(−x)5
Rewrite the expression
32(−x5)
Multiplying or dividing an odd number of negative terms equals a negative
−32x5
−y=−32x5
Change the signs both sides
y=32x5
Solution
Symmetry with respect to the origin
Show Solution
Solve the equation
x=2548y
Evaluate
y=32x5
Swap the sides of the equation
32x5=y
Multiply by the reciprocal
32x5×23=y×23
Multiply
x5=y×23
Multiply
x5=23y
Take the 5-th root on both sides of the equation
5x5=523y
Calculate
x=523y
Solution
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Evaluate
523y
Rewrite the expression
523×5y
Simplify the root
2548y
x=2548y
Show Solution
Rewrite the equation
r=0r=2424sin(θ)sec(θ)×∣sec(θ)∣r=−2424sin(θ)sec(θ)×∣sec(θ)∣
Evaluate
y=32x5
Multiply both sides of the equation by LCD
y×3=32x5×3
Use the commutative property to reorder the terms
3y=32x5×3
Simplify the equation
3y=2x5
Move the expression to the left side
3y−2x5=0
To convert the equation to polar coordinates,substitute x for rcos(θ) and y for rsin(θ)
3sin(θ)×r−2(cos(θ)×r)5=0
Factor the expression
−2cos5(θ)×r5+3sin(θ)×r=0
Factor the expression
r(−2cos5(θ)×r4+3sin(θ))=0
When the product of factors equals 0,at least one factor is 0
r=0−2cos5(θ)×r4+3sin(θ)=0
Solution
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Factor the expression
−2cos5(θ)×r4+3sin(θ)=0
Subtract the terms
−2cos5(θ)×r4+3sin(θ)−3sin(θ)=0−3sin(θ)
Evaluate
−2cos5(θ)×r4=−3sin(θ)
Divide the terms
r4=2cos5(θ)3sin(θ)
Simplify the expression
r4=23sin(θ)sec5(θ)
Evaluate the power
r=±423sin(θ)sec5(θ)
Simplify the expression
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Evaluate
423sin(θ)sec5(θ)
To take a root of a fraction,take the root of the numerator and denominator separately
4243sin(θ)sec5(θ)
Simplify the radical expression
4243sin(θ)sec(θ)×∣sec(θ)∣
Multiply by the Conjugate
42×42343sin(θ)sec(θ)×∣sec(θ)∣×423
Calculate
243sin(θ)sec(θ)×∣sec(θ)∣×423
Calculate the product
2424sin(θ)sec(θ)×∣sec(θ)∣
r=±2424sin(θ)sec(θ)×∣sec(θ)∣
Separate into possible cases
r=2424sin(θ)sec(θ)×∣sec(θ)∣r=−2424sin(θ)sec(θ)×∣sec(θ)∣
r=0r=2424sin(θ)sec(θ)×∣sec(θ)∣r=−2424sin(θ)sec(θ)×∣sec(θ)∣
Show Solution
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