Find The Inverse Function F(x)=(4x)/(9x-5) - Mathway

Enter a problem... Precalculus Examples Popular Problems Precalculus Find the Inverse f(x)=(4x)/(9x-5) Step 1Write as an equation.Step 2Interchange the variables.Step 3Solve for .Tap for more steps...Step 3.1Multiply the equation by .Step 3.2Simplify the left side.Tap for more steps...Step 3.2.1Apply the distributive property.Step 3.3Simplify the right side.Tap for more steps...Step 3.3.1Cancel the common factor of .Tap for more steps...Step 3.3.1.1Cancel the common factor.Step 3.3.1.2Rewrite the expression.Step 3.4Solve for .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 3.4.4.2.1.2Divide 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 5.2.3Combine and .Step 5.2.4Simplify the denominator.Tap for more steps...Step 5.2.4.1Multiply .Tap for more steps...Step 5.2.4.1.1Combine and .Step 5.2.4.1.2Multiply by .Step 5.2.4.2To write as a fraction with a common denominator, multiply by .Step 5.2.4.3Combine and .Step 5.2.4.4Combine the numerators over the common denominator.Step 5.2.4.5Rewrite in a factored form.Tap for more steps...Step 5.2.4.5.1Factor out of .Tap for more steps...Step 5.2.4.5.1.1Factor out of .Step 5.2.4.5.1.2Factor out of .Step 5.2.4.5.1.3Factor out of .Step 5.2.4.5.2Apply the distributive property.Step 5.2.4.5.3Multiply by .Step 5.2.4.5.4Multiply by .Step 5.2.4.5.5Subtract from .Step 5.2.4.5.6Add and .Step 5.2.4.6Multiply by .Step 5.2.5Multiply by .Step 5.2.6Multiply the numerator by the reciprocal of the denominator.Step 5.2.7Cancel the common factor of .Tap for more steps...Step 5.2.7.1Factor out of .Step 5.2.7.2Cancel the common factor.Step 5.2.7.3Rewrite the expression.Step 5.2.8Cancel the common factor of .Tap for more steps...Step 5.2.8.1Cancel the common factor.Step 5.2.8.2Rewrite 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 5.3.3Combine and .Step 5.3.4Simplify the denominator.Tap for more steps...Step 5.3.4.1Multiply .Tap for more steps...Step 5.3.4.1.1Combine and .Step 5.3.4.1.2Multiply by .Step 5.3.4.2To write as a fraction with a common denominator, multiply by .Step 5.3.4.3Combine and .Step 5.3.4.4Combine the numerators over the common denominator.Step 5.3.4.5Rewrite in a factored form.Tap for more steps...Step 5.3.4.5.1Factor out of .Tap for more steps...Step 5.3.4.5.1.1Factor out of .Step 5.3.4.5.1.2Factor out of .Step 5.3.4.5.1.3Factor out of .Step 5.3.4.5.2Apply the distributive property.Step 5.3.4.5.3Multiply by .Step 5.3.4.5.4Multiply by .Step 5.3.4.5.5Subtract from .Step 5.3.4.5.6Add and .Step 5.3.4.6Multiply by .Step 5.3.5Multiply by .Step 5.3.6Multiply the numerator by the reciprocal of the denominator.Step 5.3.7Cancel the common factor of .Tap for more steps...Step 5.3.7.1Factor out of .Step 5.3.7.2Cancel the common factor.Step 5.3.7.3Rewrite the expression.Step 5.3.8Cancel the common factor of .Tap for more steps...Step 5.3.8.1Cancel the common factor.Step 5.3.8.2Rewrite the expression.Step 5.4Since and , then is the inverse of .

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