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
Change the signs on both 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=5−23x
Calculate
y=5−23x
Simplify the root
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Evaluate
5−23x
Rewrite the expression
5−23×5x
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 even number of negative terms equals a positive
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
Change the signs on both 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=5−23y
Calculate
x=5−23y
Solution
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Evaluate
5−23y
Rewrite the expression
5−23×5y
Simplify the root
−2548y
x=−2548y
Show Solution
Rewrite the equation
r=0r=24−24sin(θ)sec(θ)×∣sec(θ)∣r=−24−24sin(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=02cos5(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=±4−23sin(θ)sec5(θ)
Simplify the expression
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Evaluate
4−23sin(θ)sec5(θ)
To take a root of a fraction,take the root of the numerator and denominator separately
424−3sin(θ)sec5(θ)
Simplify the radical expression
424−3sin(θ)sec(θ)×∣sec(θ)∣
Multiply by the Conjugate
42×4234−3sin(θ)sec(θ)×∣sec(θ)∣×423
Calculate
24−3sin(θ)sec(θ)×∣sec(θ)∣×423
Calculate the product
24−24sin(θ)sec(θ)×∣sec(θ)∣
r=±24−24sin(θ)sec(θ)×∣sec(θ)∣
Separate into possible cases
r=24−24sin(θ)sec(θ)×∣sec(θ)∣r=−24−24sin(θ)sec(θ)×∣sec(θ)∣
r=0r=24−24sin(θ)sec(θ)×∣sec(θ)∣r=−24−24sin(θ)sec(θ)×∣sec(θ)∣
Show Solution
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