Trigonometry Examples

Find the Inverse y=(x-1)^3+1
Step 1
Interchange the variables.
Step 2
Solve for .
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Step 2.1
Rewrite the equation as .
Step 2.2
Subtract from both sides of the equation.
Step 2.3
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 2.4
Add to both sides of the equation.
Step 3
Replace with to show the final answer.
Step 4
Verify if is the inverse of .
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Step 4.1
To verify the inverse, check if and .
Step 4.2
Evaluate .
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Step 4.2.1
Set up the composite result function.
Step 4.2.2
Evaluate by substituting in the value of into .
Step 4.2.3
Combine the opposite terms in .
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Step 4.2.3.1
Subtract from .
Step 4.2.3.2
Add and .
Step 4.2.4
Pull terms out from under the radical, assuming real numbers.
Step 4.2.5
Combine the opposite terms in .
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Step 4.2.5.1
Add and .
Step 4.2.5.2
Add and .
Step 4.3
Evaluate .
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Step 4.3.1
Set up the composite result function.
Step 4.3.2
Evaluate by substituting in the value of into .
Step 4.3.3
Combine the opposite terms in .
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Step 4.3.3.1
Subtract from .
Step 4.3.3.2
Add and .
Step 4.3.4
Rewrite as .
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Step 4.3.4.1
Use to rewrite as .
Step 4.3.4.2
Apply the power rule and multiply exponents, .
Step 4.3.4.3
Combine and .
Step 4.3.4.4
Cancel the common factor of .
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Step 4.3.4.4.1
Cancel the common factor.
Step 4.3.4.4.2
Rewrite the expression.
Step 4.3.4.5
Simplify.
Step 4.3.5
Combine the opposite terms in .
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Step 4.3.5.1
Add and .
Step 4.3.5.2
Add and .
Step 4.4
Since and , then is the inverse of .