Trigonometry Examples

Find the Inverse f(x)-3/5x+9
Step 1
Interchange the variables.
Step 2
Solve for .
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Step 2.1
Rewrite the equation as .
Step 2.2
Simplify each term.
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Step 2.2.1
Combine and .
Step 2.2.2
Move to the left of .
Step 2.3
Move all terms not containing to the right side of the equation.
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Step 2.3.1
Add to both sides of the equation.
Step 2.3.2
Subtract from both sides of the equation.
Step 2.4
Divide each term in by and simplify.
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Step 2.4.1
Divide each term in by .
Step 2.4.2
Simplify the left side.
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Step 2.4.2.1
Cancel the common factor of .
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Step 2.4.2.1.1
Cancel the common factor.
Step 2.4.2.1.2
Divide by .
Step 2.4.3
Simplify the right side.
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Step 2.4.3.1
Simplify each term.
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Step 2.4.3.1.1
Multiply the numerator by the reciprocal of the denominator.
Step 2.4.3.1.2
Cancel the common factor of .
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Step 2.4.3.1.2.1
Factor out of .
Step 2.4.3.1.2.2
Cancel the common factor.
Step 2.4.3.1.2.3
Rewrite the expression.
Step 2.4.3.1.3
Move the negative in front of the fraction.
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
Simplify terms.
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Step 4.2.3.1
Combine the numerators over the common denominator.
Step 4.2.3.2
Combine the opposite terms in .
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Step 4.2.3.2.1
Subtract from .
Step 4.2.3.2.2
Add and .
Step 4.2.4
Simplify each term.
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Step 4.2.4.1
Combine and .
Step 4.2.4.2
Move to the left of .
Step 4.2.5
Reorder and .
Step 4.2.6
Simplify each term.
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Step 4.2.6.1
Simplify the numerator.
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Step 4.2.6.1.1
To write as a fraction with a common denominator, multiply by .
Step 4.2.6.1.2
Combine and .
Step 4.2.6.1.3
Combine the numerators over the common denominator.
Step 4.2.6.1.4
Move to the left of .
Step 4.2.6.2
Multiply the numerator by the reciprocal of the denominator.
Step 4.2.6.3
Multiply by .
Step 4.2.7
To write as a fraction with a common denominator, multiply by .
Step 4.2.8
Simplify terms.
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Step 4.2.8.1
Multiply by .
Step 4.2.8.2
Combine the numerators over the common denominator.
Step 4.2.9
Simplify the numerator.
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Step 4.2.9.1
Add and .
Step 4.2.9.2
Add and .
Step 4.2.10
Cancel the common factor of .
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Step 4.2.10.1
Cancel the common factor.
Step 4.2.10.2
Rewrite the expression.
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
Simplify each term.
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Step 4.3.3.1
Apply the distributive property.
Step 4.3.3.2
Simplify.
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Step 4.3.3.2.1
Cancel the common factor of .
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Step 4.3.3.2.1.1
Cancel the common factor.
Step 4.3.3.2.1.2
Rewrite the expression.
Step 4.3.3.2.2
Combine and .
Step 4.3.3.2.3
Cancel the common factor of .
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Step 4.3.3.2.3.1
Move the leading negative in into the numerator.
Step 4.3.3.2.3.2
Cancel the common factor.
Step 4.3.3.2.3.3
Rewrite the expression.
Step 4.3.3.3
Combine and .
Step 4.3.3.4
Move to the left of .
Step 4.3.4
Combine the opposite terms in .
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Step 4.3.4.1
Subtract from .
Step 4.3.4.2
Add and .
Step 4.3.4.3
Add and .
Step 4.3.4.4
Add and .
Step 4.4
Since and , then is the inverse of .