Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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f−1(x)=−10350x+850
Evaluate
y=−2x2×10x−17
Simplify
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Evaluate
−2x2×10x−17
Multiply
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Evaluate
−2x2×10x
Multiply the terms
−20x2×x
Multiply the terms with the same base by adding their exponents
−20x2+1
Add the numbers
−20x3
−20x3−17
y=−20x3−17
Interchange x and y
x=−20y3−17
Swap the sides of the equation
−20y3−17=x
Move the constant to the right-hand side and change its sign
−20y3=x+17
Change the signs on both sides of the equation
20y3=−x−17
Divide both sides
2020y3=20−x−17
Divide the numbers
y3=20−x−17
Use b−a=−ba=−ba to rewrite the fraction
y3=−20x+17
Take the 3-th root on both sides of the equation
3y3=3−20x+17
Calculate
y=3−20x+17
Simplify the root
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Evaluate
3−20x+17
To take a root of a fraction,take the root of the numerator and denominator separately
3203−x−17
Simplify the radical expression
320−3x+17
Simplify the radical expression
−3203x+17
Multiply by the Conjugate
−320×32023x+17×3202
Calculate
−203x+17×3202
Calculate
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Evaluate
3x+17×3202
The product of roots with the same index is equal to the root of the product
3(x+17)×202
Calculate the product
3400x+6800
Factor the expression
3400(x+17)
The root of a product is equal to the product of the roots of each factor
3400×3x+17
Evaluate the root
2350×3x+17
Calculate the product
2350x+850
−202350x+850
Cancel out the common factor 2
−10350x+850
y=−10350x+850
Solution
f−1(x)=−10350x+850
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=−2x210x−17
Simplify the expression
y=−20x3−17
To test if the graph of y=−20x3−17 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=−20(−x)3−17
Simplify
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Evaluate
−20(−x)3−17
Multiply the terms
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Evaluate
−20(−x)3
Rewrite the expression
−20(−x3)
Multiply the numbers
20x3
20x3−17
−y=20x3−17
Change the signs both sides
y=−20x3+17
Solution
Not symmetry with respect to the origin
Show Solution

Solve the equation
Solve for x
Solve for y
x=−10350y+850
Evaluate
y=−2x2×10x−17
Simplify
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Evaluate
−2x2×10x−17
Multiply
More Steps

Evaluate
−2x2×10x
Multiply the terms
−20x2×x
Multiply the terms with the same base by adding their exponents
−20x2+1
Add the numbers
−20x3
−20x3−17
y=−20x3−17
Swap the sides of the equation
−20x3−17=y
Move the constant to the right-hand side and change its sign
−20x3=y+17
Change the signs on both sides of the equation
20x3=−y−17
Divide both sides
2020x3=20−y−17
Divide the numbers
x3=20−y−17
Use b−a=−ba=−ba to rewrite the fraction
x3=−20y+17
Take the 3-th root on both sides of the equation
3x3=3−20y+17
Calculate
x=3−20y+17
Solution
More Steps

Evaluate
3−20y+17
To take a root of a fraction,take the root of the numerator and denominator separately
3203−y−17
Simplify the radical expression
320−3y+17
Simplify the radical expression
−3203y+17
Multiply by the Conjugate
−320×32023y+17×3202
Calculate
−203y+17×3202
Calculate
More Steps

Evaluate
3y+17×3202
The product of roots with the same index is equal to the root of the product
3(y+17)×202
Calculate the product
3400y+6800
Factor the expression
3400(y+17)
The root of a product is equal to the product of the roots of each factor
3400×3y+17
Evaluate the root
2350×3y+17
Calculate the product
2350y+850
−202350y+850
Cancel out the common factor 2
−10350y+850
x=−10350y+850
Show Solution
