Find the Inverse f(x)=3x-4+2x^2

Math
Replace with .
Interchange the variables.
Solve for .
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Rewrite the equation as .
Move to the left side of the equation by subtracting it from both sides.
Use the quadratic formula to find the solutions.
Substitute the values , , and into the quadratic formula and solve for .
Simplify.
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Simplify the numerator.
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Raise to the power of .
Apply the distributive property.
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Add and .
Multiply by .
Simplify the expression to solve for the portion of the .
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Simplify the numerator.
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Raise to the power of .
Apply the distributive property.
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Add and .
Multiply by .
Change the to .
Rewrite as .
Factor out of .
Factor out of .
Move the negative in front of the fraction.
Simplify the expression to solve for the portion of the .
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Simplify the numerator.
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Raise to the power of .
Apply the distributive property.
Multiply by .
Multiply by .
Apply the distributive property.
Multiply by .
Multiply by .
Add and .
Multiply by .
Change the to .
Factor out of .
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Reorder and .
Rewrite as .
Factor out of .
Factor out of .
Rewrite as .
Move the negative in front of the fraction.
The final answer is the combination of both solutions.
Solve for and replace with .
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Replace the with to show the final answer.
Set up the composite result function.
Evaluate by substituting in the value of into .
Simplify the numerator.
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Apply the distributive property.
Simplify.
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Multiply by .
Multiply by .
Multiply by .
Subtract from .
Reorder terms.
Factor using the perfect square rule.
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Rewrite as .
Rewrite as .
Check the middle term by multiplying and compare this result with the middle term in the original expression.
Simplify.
Factor using the perfect square trinomial rule , where and .
Pull terms out from under the radical, assuming positive real numbers.
Apply the distributive property.
Multiply by .
Multiply by .
Subtract from .
Add and .
Cancel the common factor of and .
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Factor out of .
Cancel the common factors.
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Since , is the inverse of .
Find the Inverse f(x)=3x-4+2x^2

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