Find The Inverse F(x)=(6x-1)/(2x+3) | Mathway

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Calculus Examples Popular Problems Calculus Find the Inverse f(x)=(6x-1)/(2x+3) Step 1Write as an equation.Step 2Interchange the variables.Step 3Solve for .Tap for more steps...Step 3.1Rewrite the equation as .Step 3.2Find the LCD of the terms in the equation.Tap for more steps...Step 3.2.1Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.Step 3.2.2Remove parentheses.Step 3.2.3The LCM of one and any expression is the expression.Step 3.3Multiply each term in by to eliminate the fractions.Tap for more steps...Step 3.3.1Multiply each term in by .Step 3.3.2Simplify the left side.Tap for more steps...Step 3.3.2.1Cancel the common factor of .Tap for more steps...Step 3.3.2.1.1Cancel the common factor.Step 3.3.2.1.2Rewrite the expression.Step 3.3.3Simplify the right side.Tap for more steps...Step 3.3.3.1Apply the distributive property.Step 3.3.3.2Reorder.Tap for more steps...Step 3.3.3.2.1Rewrite using the commutative property of multiplication.Step 3.3.3.2.2Move to the left of .Step 3.4Solve the equation.Tap for more steps...Step 3.4.1Subtract from both sides of the equation.Step 3.4.2Add to both sides of the equation.Step 3.4.3Factor out of .Tap for more steps...Step 3.4.3.1Factor out of .Step 3.4.3.2Factor out of .Step 3.4.3.3Factor out of .Step 3.4.4Divide each term in by and simplify.Tap for more steps...Step 3.4.4.1Divide each term in by .Step 3.4.4.2Simplify the left side.Tap for more steps...Step 3.4.4.2.1Cancel the common factor of .Tap for more steps...Step 3.4.4.2.1.1Cancel the common factor.Step 3.4.4.2.1.2Rewrite the expression.Step 3.4.4.2.2Cancel the common factor of .Tap for more steps...Step 3.4.4.2.2.1Cancel the common factor.Step 3.4.4.2.2.2Divide by .Step 4Replace with to show the final answer.Step 5Verify if is the inverse of .Tap for more steps...Step 5.1To verify the inverse, check if and .Step 5.2Evaluate .Tap for more steps...Step 5.2.1Set up the composite result function.Step 5.2.2Evaluate by substituting in the value of into .Step 5.2.3Simplify terms.Tap for more steps...Step 5.2.3.1Combine the numerators over the common denominator.Step 5.2.3.2Combine and .Step 5.2.3.3Write as a fraction with a common denominator.Step 5.2.3.4Combine the numerators over the common denominator.Step 5.2.4Simplify the numerator.Tap for more steps...Step 5.2.4.1Apply the distributive property.Step 5.2.4.2Multiply by .Step 5.2.4.3Multiply by .Step 5.2.4.4Add and .Step 5.2.4.5Add and .Step 5.2.4.6Add and .Step 5.2.5Multiply the numerator by the reciprocal of the denominator.Step 5.2.6Simplify terms.Tap for more steps...Step 5.2.6.1Cancel the common factor of .Tap for more steps...Step 5.2.6.1.1Factor out of .Step 5.2.6.1.2Cancel the common factor.Step 5.2.6.1.3Rewrite the expression.Step 5.2.6.2Multiply by .Step 5.2.7Simplify the denominator.Tap for more steps...Step 5.2.7.1To write as a fraction with a common denominator, multiply by .Step 5.2.7.2Combine the numerators over the common denominator.Step 5.2.7.3Rewrite in a factored form.Tap for more steps...Step 5.2.7.3.1Apply the distributive property.Step 5.2.7.3.2Multiply by .Step 5.2.7.3.3Multiply by .Step 5.2.7.3.4Apply the distributive property.Step 5.2.7.3.5Multiply by .Step 5.2.7.3.6Multiply by .Step 5.2.7.3.7Subtract from .Step 5.2.7.3.8Add and .Step 5.2.7.3.9Add and .Step 5.2.8Factor out of .Step 5.2.9Cancel the common factor of .Tap for more steps...Step 5.2.9.1Cancel the common factor.Step 5.2.9.2Rewrite the expression.Step 5.2.10Cancel the common factor of .Tap for more steps...Step 5.2.10.1Factor out of .Step 5.2.10.2Cancel the common factor.Step 5.2.10.3Rewrite the expression.Step 5.3Evaluate .Tap for more steps...Step 5.3.1Set up the composite result function.Step 5.3.2Evaluate by substituting in the value of into .Step 5.3.3Simplify the numerator.Tap for more steps...Step 5.3.3.1Apply the distributive property.Step 5.3.3.2Cancel the common factor of .Tap for more steps...Step 5.3.3.2.1Factor out of .Step 5.3.3.2.2Cancel the common factor.Step 5.3.3.2.3Rewrite the expression.Step 5.3.3.3Combine and .Step 5.3.3.4Multiply by .Step 5.3.3.5Cancel the common factor of .Tap for more steps...Step 5.3.3.5.1Factor out of .Step 5.3.3.5.2Cancel the common factor.Step 5.3.3.5.3Rewrite the expression.Step 5.3.3.6Combine and .Step 5.3.3.7Combine the numerators over the common denominator.Step 5.3.3.8Factor out of .Tap for more steps...Step 5.3.3.8.1Factor out of .Step 5.3.3.8.2Factor out of .Step 5.3.3.8.3Factor out of .Step 5.3.3.9To write as a fraction with a common denominator, multiply by .Step 5.3.3.10Combine and .Step 5.3.3.11Combine the numerators over the common denominator.Step 5.3.3.12Reorder terms.Step 5.3.3.13Rewrite in a factored form.Tap for more steps...Step 5.3.3.13.1Apply the distributive property.Step 5.3.3.13.2Multiply by .Step 5.3.3.13.3Multiply by .Step 5.3.3.13.4Apply the distributive property.Step 5.3.3.13.5Multiply by .Step 5.3.3.13.6Multiply .Tap for more steps...Step 5.3.3.13.6.1Multiply by .Step 5.3.3.13.6.2Multiply by .Step 5.3.3.13.7Add and .Step 5.3.3.13.8Subtract from .Step 5.3.3.13.9Add and .Step 5.3.4Simplify the denominator.Tap for more steps...Step 5.3.4.1Apply the distributive property.Step 5.3.4.2Cancel the common factor of .Tap for more steps...Step 5.3.4.2.1Cancel the common factor.Step 5.3.4.2.2Rewrite the expression.Step 5.3.4.3Cancel the common factor of .Tap for more steps...Step 5.3.4.3.1Cancel the common factor.Step 5.3.4.3.2Rewrite the expression.Step 5.3.4.4Combine the numerators over the common denominator.Step 5.3.4.5To write as a fraction with a common denominator, multiply by .Step 5.3.4.6Combine the numerators over the common denominator.Step 5.3.4.7Reorder terms.Step 5.3.4.8Rewrite in a factored form.Tap for more steps...Step 5.3.4.8.1Apply the distributive property.Step 5.3.4.8.2Multiply by .Step 5.3.4.8.3Multiply by .Step 5.3.4.8.4Subtract from .Step 5.3.4.8.5Add and .Step 5.3.4.8.6Add and .Step 5.3.5Multiply the numerator by the reciprocal of the denominator.Step 5.3.6Cancel the common factor of .Tap for more steps...Step 5.3.6.1Factor out of .Step 5.3.6.2Cancel the common factor.Step 5.3.6.3Rewrite the expression.Step 5.3.7Multiply by .Step 5.3.8Cancel the common factor of .Tap for more steps...Step 5.3.8.1Cancel the common factor.Step 5.3.8.2Divide by .Step 5.4Since and , then is the inverse of .

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