Trigonometry Examples

Find the Inverse f(x)=-3/8x^7
Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Solve for .
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Step 3.1
Rewrite the equation as .
Step 3.2
Multiply both sides of the equation by .
Step 3.3
Simplify both sides of the equation.
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Step 3.3.1
Simplify the left side.
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Step 3.3.1.1
Simplify .
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Step 3.3.1.1.1
Combine and .
Step 3.3.1.1.2
Cancel the common factor of .
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Step 3.3.1.1.2.1
Move the leading negative in into the numerator.
Step 3.3.1.1.2.2
Move the leading negative in into the numerator.
Step 3.3.1.1.2.3
Factor out of .
Step 3.3.1.1.2.4
Cancel the common factor.
Step 3.3.1.1.2.5
Rewrite the expression.
Step 3.3.1.1.3
Cancel the common factor of .
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Step 3.3.1.1.3.1
Factor out of .
Step 3.3.1.1.3.2
Cancel the common factor.
Step 3.3.1.1.3.3
Rewrite the expression.
Step 3.3.1.1.4
Multiply.
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Step 3.3.1.1.4.1
Multiply by .
Step 3.3.1.1.4.2
Multiply by .
Step 3.3.2
Simplify the right side.
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Step 3.3.2.1
Simplify .
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Step 3.3.2.1.1
Combine and .
Step 3.3.2.1.2
Move to the left of .
Step 3.4
Take the specified root of both sides of the equation to eliminate the exponent on the left side.
Step 3.5
Simplify .
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Step 3.5.1
Rewrite as .
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Step 3.5.1.1
Rewrite as .
Step 3.5.1.2
Rewrite as .
Step 3.5.2
Pull terms out from under the radical.
Step 3.5.3
Raise to the power of .
Step 3.5.4
Rewrite as .
Step 4
Replace with to show the final answer.
Step 5
Verify if is the inverse of .
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Step 5.1
To verify the inverse, check if and .
Step 5.2
Evaluate .
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Step 5.2.1
Set up the composite result function.
Step 5.2.2
Evaluate by substituting in the value of into .
Step 5.2.3
Simplify the numerator.
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Step 5.2.3.1
Multiply by .
Step 5.2.3.2
Combine and .
Step 5.2.3.3
Combine and .
Step 5.2.3.4
Reduce the expression by cancelling the common factors.
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Step 5.2.3.4.1
Reduce the expression by cancelling the common factors.
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Step 5.2.3.4.1.1
Factor out of .
Step 5.2.3.4.1.2
Factor out of .
Step 5.2.3.4.1.3
Cancel the common factor.
Step 5.2.3.4.1.4
Rewrite the expression.
Step 5.2.3.4.2
Divide by .
Step 5.2.3.5
Combine exponents.
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Step 5.2.3.5.1
Factor out negative.
Step 5.2.3.5.2
Multiply by .
Step 5.2.3.6
Rewrite as .
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Step 5.2.3.6.1
Rewrite as .
Step 5.2.3.6.2
Rewrite as .
Step 5.2.3.6.3
Move .
Step 5.2.3.6.4
Rewrite as .
Step 5.2.3.7
Pull terms out from under the radical.
Step 5.2.4
Cancel the common factor of .
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Step 5.2.4.1
Cancel the common factor.
Step 5.2.4.2
Divide by .
Step 5.3
Evaluate .
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Step 5.3.1
Set up the composite result function.
Step 5.3.2
Evaluate by substituting in the value of into .
Step 5.3.3
Use the power rule to distribute the exponent.
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Step 5.3.3.1
Apply the product rule to .
Step 5.3.3.2
Apply the product rule to .
Step 5.3.4
Multiply by by adding the exponents.
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Step 5.3.4.1
Move .
Step 5.3.4.2
Multiply by .
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Step 5.3.4.2.1
Raise to the power of .
Step 5.3.4.2.2
Use the power rule to combine exponents.
Step 5.3.4.3
Add and .
Step 5.3.5
Rewrite as .
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Step 5.3.5.1
Use to rewrite as .
Step 5.3.5.2
Apply the power rule and multiply exponents, .
Step 5.3.5.3
Combine and .
Step 5.3.5.4
Cancel the common factor of .
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Step 5.3.5.4.1
Cancel the common factor.
Step 5.3.5.4.2
Rewrite the expression.
Step 5.3.5.5
Simplify.
Step 5.3.6
Rewrite as .
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Step 5.3.6.1
Use to rewrite as .
Step 5.3.6.2
Apply the power rule and multiply exponents, .
Step 5.3.6.3
Combine and .
Step 5.3.6.4
Cancel the common factor of .
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Step 5.3.6.4.1
Cancel the common factor.
Step 5.3.6.4.2
Rewrite the expression.
Step 5.3.6.5
Evaluate the exponent.
Step 5.3.7
Simplify the expression.
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Step 5.3.7.1
Raise to the power of .
Step 5.3.7.2
Multiply by .
Step 5.3.8
Cancel the common factor of .
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Step 5.3.8.1
Cancel the common factor.
Step 5.3.8.2
Rewrite the expression.
Step 5.3.9
Cancel the common factor of .
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Step 5.3.9.1
Factor out of .
Step 5.3.9.2
Cancel the common factor.
Step 5.3.9.3
Rewrite the expression.
Step 5.4
Since and , then is the inverse of .