Find The Inverse Function F(x)=5x^2+7 - Mathway

Enter a problem... Precalculus Examples Popular Problems Precalculus Find the Inverse f(x)=5x^2+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 3.3Divide each term in by and simplify.Tap for more steps...Step 3.3.1Divide 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 3.3.2.1.2Divide by .Step 3.3.3Simplify the right side.Tap for more steps...Step 3.3.3.1Move the negative in front of the fraction.Step 3.4Take the specified root of both sides of the equation to eliminate the exponent on the left side.Step 3.5Simplify .Tap for more steps...Step 3.5.1Combine the numerators over the common denominator.Step 3.5.2Rewrite as .Step 3.5.3Multiply by .Step 3.5.4Combine and simplify the denominator.Tap for more steps...Step 3.5.4.1Multiply by .Step 3.5.4.2Raise to the power of .Step 3.5.4.3Raise to the power of .Step 3.5.4.4Use the power rule to combine exponents.Step 3.5.4.5Add and .Step 3.5.4.6Rewrite as .Tap for more steps...Step 3.5.4.6.1Use to rewrite as .Step 3.5.4.6.2Apply the power rule and multiply exponents, .Step 3.5.4.6.3Combine and .Step 3.5.4.6.4Cancel the common factor of .Tap for more steps...Step 3.5.4.6.4.1Cancel the common factor.Step 3.5.4.6.4.2Rewrite the expression.Step 3.5.4.6.5Evaluate the exponent.Step 3.5.5Combine using the product rule for radicals.Step 3.5.6Reorder factors in .Step 3.6The complete solution is the result of both the positive and negative portions of the solution.Tap for more steps...Step 3.6.1First, use the positive value of the to find the first solution.Step 3.6.2Next, use the negative value of the to find the second solution.Step 3.6.3The complete solution is the result of both the positive and negative portions of the solution.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 5.3.2Solve for .Tap for more steps...Step 5.3.2.1Divide each term in by and simplify.Tap for more steps...Step 5.3.2.1.1Divide each term in by .Step 5.3.2.1.2Simplify the left side.Tap for more steps...Step 5.3.2.1.2.1Cancel the common factor of .Tap for more steps...Step 5.3.2.1.2.1.1Cancel the common factor.Step 5.3.2.1.2.1.2Divide by .Step 5.3.2.1.3Simplify the right side.Tap for more steps...Step 5.3.2.1.3.1Divide by .Step 5.3.2.2Add to 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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