Find The Inverse F(x)=x^2+8x-7 | Mathway

Enter a problem... Trigonometry Examples Popular Problems Trigonometry Find the Inverse f(x)=x^2+8x-7 Step 1Write as an equation.Step 2Interchange the variables.Step 3Solve for .Tap for more steps...Step 3.1Rewrite the equation as .Step 3.2Subtract from both sides of the equation.Step 3.3Use the quadratic formula to find the solutions.Step 3.4Substitute the values , , and into the quadratic formula and solve for .Step 3.5Simplify.Tap for more steps...Step 3.5.1Simplify the numerator.Tap for more steps...Step 3.5.1.1Raise to the power of .Step 3.5.1.2Multiply by .Step 3.5.1.3Apply the distributive property.Step 3.5.1.4Multiply by .Step 3.5.1.5Multiply by .Step 3.5.1.6Add and .Step 3.5.1.7Factor out of .Tap for more steps...Step 3.5.1.7.1Factor out of .Step 3.5.1.7.2Factor out of .Step 3.5.1.8Rewrite as .Step 3.5.1.9Pull terms out from under the radical.Step 3.5.2Multiply by .Step 3.5.3Simplify .Step 3.6Simplify the expression to solve for the portion of the .Tap for more steps...Step 3.6.1Simplify the numerator.Tap for more steps...Step 3.6.1.1Raise to the power of .Step 3.6.1.2Multiply by .Step 3.6.1.3Apply the distributive property.Step 3.6.1.4Multiply by .Step 3.6.1.5Multiply by .Step 3.6.1.6Add and .Step 3.6.1.7Factor out of .Tap for more steps...Step 3.6.1.7.1Factor out of .Step 3.6.1.7.2Factor out of .Step 3.6.1.8Rewrite as .Step 3.6.1.9Pull terms out from under the radical.Step 3.6.2Multiply by .Step 3.6.3Simplify .Step 3.6.4Change the to .Step 3.7Simplify the expression to solve for the portion of the .Tap for more steps...Step 3.7.1Simplify the numerator.Tap for more steps...Step 3.7.1.1Raise to the power of .Step 3.7.1.2Multiply by .Step 3.7.1.3Apply the distributive property.Step 3.7.1.4Multiply by .Step 3.7.1.5Multiply by .Step 3.7.1.6Add and .Step 3.7.1.7Factor out of .Tap for more steps...Step 3.7.1.7.1Factor out of .Step 3.7.1.7.2Factor out of .Step 3.7.1.8Rewrite as .Step 3.7.1.9Pull terms out from under the radical.Step 3.7.2Multiply by .Step 3.7.3Simplify .Step 3.7.4Change the to .Step 3.8The final answer is the combination of both solutions.Step 4Replace with to show the final answer.Step 5Verify if is the inverse of .Tap for more steps...Step 5.1The domain of the inverse is the range of the original function and vice versa. Find the domain and the range of and and compare them.Step 5.2Find the range of .Tap for more steps...Step 5.2.1The range is the set of all valid values. Use the graph to find the range.Interval Notation:Step 5.3Find the domain of .Tap for more steps...Step 5.3.1Set the radicand in greater than or equal to to find where the expression is defined.Step 5.3.2Subtract from both sides of the inequality.Step 5.3.3The domain is all values of that make the expression defined.Step 5.4Find the domain of .Tap for more steps...Step 5.4.1The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.Step 5.5Since the domain of is the range of and the range of is the domain of , then is the inverse of .Step 6

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