Question
Function
Find the inverse
Evaluate the derivative
Find the domain
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f−1(x)=234x+16
Evaluate
y=x2×2x−4
Simplify
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Evaluate
x2×2x−4
Multiply
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Evaluate
x2×2x
Multiply the terms with the same base by adding their exponents
x2+1×2
Add the numbers
x3×2
Use the commutative property to reorder the terms
2x3
2x3−4
y=2x3−4
Interchange x and y
x=2y3−4
Swap the sides of the equation
2y3−4=x
Move the constant to the right-hand side and change its sign
2y3=x+4
Divide both sides
22y3=2x+4
Divide the numbers
y3=2x+4
Take the 3-th root on both sides of the equation
3y3=32x+4
Calculate
y=32x+4
Simplify the root
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Evaluate
32x+4
To take a root of a fraction,take the root of the numerator and denominator separately
323x+4
Multiply by the Conjugate
32×3223x+4×322
Calculate
23x+4×322
Calculate
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Evaluate
3x+4×322
The product of roots with the same index is equal to the root of the product
3(x+4)×22
Calculate the product
34x+16
234x+16
y=234x+16
Solution
f−1(x)=234x+16
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=x22x−4
Simplify the expression
y=2x3−4
To test if the graph of y=2x3−4 is symmetry with respect to the origin,substitute -x for x and -y for y
−y=2(−x)3−4
Simplify
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Evaluate
2(−x)3−4
Multiply the terms
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Evaluate
2(−x)3
Rewrite the expression
2(−x3)
Multiply the numbers
−2x3
−2x3−4
−y=−2x3−4
Change the signs both sides
y=2x3+4
Solution
Not symmetry with respect to the origin
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Solve the equation
Solve for x
Solve for y
x=234y+16
Evaluate
y=x2×2x−4
Simplify
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Evaluate
x2×2x−4
Multiply
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Evaluate
x2×2x
Multiply the terms with the same base by adding their exponents
x2+1×2
Add the numbers
x3×2
Use the commutative property to reorder the terms
2x3
2x3−4
y=2x3−4
Swap the sides of the equation
2x3−4=y
Move the constant to the right-hand side and change its sign
2x3=y+4
Divide both sides
22x3=2y+4
Divide the numbers
x3=2y+4
Take the 3-th root on both sides of the equation
3x3=32y+4
Calculate
x=32y+4
Solution
More Steps

Evaluate
32y+4
To take a root of a fraction,take the root of the numerator and denominator separately
323y+4
Multiply by the Conjugate
32×3223y+4×322
Calculate
23y+4×322
Calculate
More Steps

Evaluate
3y+4×322
The product of roots with the same index is equal to the root of the product
3(y+4)×22
Calculate the product
34y+16
234y+16
x=234y+16
Show Solution
