Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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f−1(x)=−2103441x+35280
Evaluate
y=−42x2×500x−80
Simplify
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Evaluate
−42x2×500x−80
Multiply
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Evaluate
−42x2×500x
Multiply the terms
−21000x2×x
Multiply the terms with the same base by adding their exponents
−21000x2+1
Add the numbers
−21000x3
−21000x3−80
y=−21000x3−80
Interchange x and y
x=−21000y3−80
Swap the sides of the equation
−21000y3−80=x
Move the constant to the right-hand side and change its sign
−21000y3=x+80
Change the signs on both sides of the equation
21000y3=−x−80
Divide both sides
2100021000y3=21000−x−80
Divide the numbers
y3=21000−x−80
Use b−a=−ba=−ba to rewrite the fraction
y3=−21000x+80
Take the 3-th root on both sides of the equation
3y3=3−21000x+80
Calculate
y=3−21000x+80
Simplify the root
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Evaluate
3−21000x+80
To take a root of a fraction,take the root of the numerator and denominator separately
3210003−x−80
Simplify the radical expression
321000−3x+80
Simplify the radical expression
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Evaluate
321000
Write the expression as a product where the root of one of the factors can be evaluated
31000×21
Write the number in exponential form with the base of 10
3103×21
The root of a product is equal to the product of the roots of each factor
3103×321
Reduce the index of the radical and exponent with 3
10321
−103213x+80
Multiply by the Conjugate
−10321×32123x+80×3212
Calculate
−10×213x+80×3212
Calculate
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Evaluate
3x+80×3212
The product of roots with the same index is equal to the root of the product
3(x+80)×212
Calculate the product
3441x+35280
−10×213441x+35280
Calculate
−2103441x+35280
y=−2103441x+35280
Solution
f−1(x)=−2103441x+35280
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
Not symmetry with respect to the origin
Evaluate
y=−42x2500x−80
Simplify the expression
y=−21000x3−80
To test if the graph of y=−21000x3−80 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=−21000(−x)3−80
Simplify
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Evaluate
−21000(−x)3−80
Multiply the terms
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Evaluate
−21000(−x)3
Rewrite the expression
−21000(−x3)
Multiply the numbers
21000x3
21000x3−80
−y=21000x3−80
Change the signs both sides
y=−21000x3+80
Solution
Not symmetry with respect to the origin
Show Solution

Solve the equation
Solve for x
Solve for y
x=−2103441y+35280
Evaluate
y=−42x2×500x−80
Simplify
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Evaluate
−42x2×500x−80
Multiply
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Evaluate
−42x2×500x
Multiply the terms
−21000x2×x
Multiply the terms with the same base by adding their exponents
−21000x2+1
Add the numbers
−21000x3
−21000x3−80
y=−21000x3−80
Swap the sides of the equation
−21000x3−80=y
Move the constant to the right-hand side and change its sign
−21000x3=y+80
Change the signs on both sides of the equation
21000x3=−y−80
Divide both sides
2100021000x3=21000−y−80
Divide the numbers
x3=21000−y−80
Use b−a=−ba=−ba to rewrite the fraction
x3=−21000y+80
Take the 3-th root on both sides of the equation
3x3=3−21000y+80
Calculate
x=3−21000y+80
Solution
More Steps

Evaluate
3−21000y+80
To take a root of a fraction,take the root of the numerator and denominator separately
3210003−y−80
Simplify the radical expression
321000−3y+80
Simplify the radical expression
More Steps

Evaluate
321000
Write the expression as a product where the root of one of the factors can be evaluated
31000×21
Write the number in exponential form with the base of 10
3103×21
The root of a product is equal to the product of the roots of each factor
3103×321
Reduce the index of the radical and exponent with 3
10321
−103213y+80
Multiply by the Conjugate
−10321×32123y+80×3212
Calculate
−10×213y+80×3212
Calculate
More Steps

Evaluate
3y+80×3212
The product of roots with the same index is equal to the root of the product
3(y+80)×212
Calculate the product
3441y+35280
−10×213441y+35280
Calculate
−2103441y+35280
x=−2103441y+35280
Show Solution
