Replace with .

Interchange the variables.

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.

Simplify the numerator.

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 .

Simplify the numerator.

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 .

Simplify the numerator.

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 .

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.

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.

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Multiply by .

Subtract from .

Reorder terms.

Factor using the perfect square rule.

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 .

Factor out of .

Cancel the common factors.

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