Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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f−1(x)=−232x+6
Evaluate
y=−x2×4x−3
Simplify
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Evaluate
−x2×4x−3
Multiply
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Evaluate
−x2×4x
Multiply the terms with the same base by adding their exponents
−x2+1×4
Add the numbers
−x3×4
Use the commutative property to reorder the terms
−4x3
−4x3−3
y=−4x3−3
Interchange x and y
x=−4y3−3
Swap the sides of the equation
−4y3−3=x
Move the constant to the right-hand side and change its sign
−4y3=x+3
Change the signs on both sides of the equation
4y3=−x−3
Divide both sides
44y3=4−x−3
Divide the numbers
y3=4−x−3
Use b−a=−ba=−ba to rewrite the fraction
y3=−4x+3
Take the 3-th root on both sides of the equation
3y3=3−4x+3
Calculate
y=3−4x+3
Simplify the root
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Evaluate
3−4x+3
To take a root of a fraction,take the root of the numerator and denominator separately
343−x−3
Simplify the radical expression
34−3x+3
Simplify the radical expression
−343x+3
Multiply by the Conjugate
−34×3423x+3×342
Calculate
−223x+3×342
Calculate
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Evaluate
3x+3×342
The product of roots with the same index is equal to the root of the product
3(x+3)×42
Calculate the product
316x+48
Factor the expression
316(x+3)
The root of a product is equal to the product of the roots of each factor
316×3x+3
Evaluate the root
232×3x+3
Calculate the product
232x+6
−22232x+6
Reduce the fraction
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Evaluate
222
Use the product rule aman=an−m to simplify the expression
22−11
Subtract the terms
211
Simplify
21
−232x+6
y=−232x+6
Solution
f−1(x)=−232x+6
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=−x24x−3
Simplify the expression
y=−4x3−3
To test if the graph of y=−4x3−3 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=−4(−x)3−3
Simplify
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Evaluate
−4(−x)3−3
Multiply the terms
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Evaluate
−4(−x)3
Rewrite the expression
−4(−x3)
Multiply the numbers
4x3
4x3−3
−y=4x3−3
Change the signs both sides
y=−4x3+3
Solution
Not symmetry with respect to the origin
Show Solution

Solve the equation
Solve for x
Solve for y
x=−232y+6
Evaluate
y=−x2×4x−3
Simplify
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Evaluate
−x2×4x−3
Multiply
More Steps

Evaluate
−x2×4x
Multiply the terms with the same base by adding their exponents
−x2+1×4
Add the numbers
−x3×4
Use the commutative property to reorder the terms
−4x3
−4x3−3
y=−4x3−3
Swap the sides of the equation
−4x3−3=y
Move the constant to the right-hand side and change its sign
−4x3=y+3
Change the signs on both sides of the equation
4x3=−y−3
Divide both sides
44x3=4−y−3
Divide the numbers
x3=4−y−3
Use b−a=−ba=−ba to rewrite the fraction
x3=−4y+3
Take the 3-th root on both sides of the equation
3x3=3−4y+3
Calculate
x=3−4y+3
Solution
More Steps

Evaluate
3−4y+3
To take a root of a fraction,take the root of the numerator and denominator separately
343−y−3
Simplify the radical expression
34−3y+3
Simplify the radical expression
−343y+3
Multiply by the Conjugate
−34×3423y+3×342
Calculate
−223y+3×342
Calculate
More Steps

Evaluate
3y+3×342
The product of roots with the same index is equal to the root of the product
3(y+3)×42
Calculate the product
316y+48
Factor the expression
316(y+3)
The root of a product is equal to the product of the roots of each factor
316×3y+3
Evaluate the root
232×3y+3
Calculate the product
232y+6
−22232y+6
Reduce the fraction
More Steps

Evaluate
222
Use the product rule aman=an−m to simplify the expression
22−11
Subtract the terms
211
Simplify
21
−232y+6
x=−232y+6
Show Solution
