Precalculus Examples

Find the Inverse y = square root of x+5
Step 1
Interchange the variables.
Step 2
Solve for .
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Rewrite the equation as .
To remove the radical on the left side of the equation, square both sides of the equation.
Simplify each side of the equation.
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Use to rewrite as .
Simplify the left side.
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Simplify .
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Multiply the exponents in .
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Apply the power rule and multiply exponents, .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Simplify.
Subtract from both sides of the equation.
Step 3
Replace with to show the final answer.
Step 4
Verify if is the inverse of .
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To verify the inverse, check if and .
Evaluate .
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Set up the composite result function.
Evaluate by substituting in the value of into .
Rewrite as .
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Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Simplify.
Combine the opposite terms in .
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Subtract from .
Add and .
Evaluate .
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Set up the composite result function.
Evaluate by substituting in the value of into .
Add and .
Add and .
Pull terms out from under the radical, assuming positive real numbers.
Since and , then is the inverse of .
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