Precalculus Examples

Find the Inverse e^x+2
Step 1
Interchange the variables.
Step 2
Solve for .
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Step 2.1
Rewrite the equation as .
Step 2.2
Subtract from both sides of the equation.
Step 2.3
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 2.4
Expand the left side.
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Step 2.4.1
Expand by moving outside the logarithm.
Step 2.4.2
The natural logarithm of is .
Step 2.4.3
Multiply by .
Step 3
Replace with to show the final answer.
Step 4
Verify if is the inverse of .
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Step 4.1
To verify the inverse, check if and .
Step 4.2
Evaluate .
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Step 4.2.1
Set up the composite result function.
Step 4.2.2
Evaluate by substituting in the value of into .
Step 4.2.3
Combine the opposite terms in .
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Step 4.2.3.1
Subtract from .
Step 4.2.3.2
Add and .
Step 4.2.4
Use logarithm rules to move out of the exponent.
Step 4.2.5
The natural logarithm of is .
Step 4.2.6
Multiply by .
Step 4.3
Evaluate .
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Step 4.3.1
Set up the composite result function.
Step 4.3.2
Evaluate by substituting in the value of into .
Step 4.3.3
Exponentiation and log are inverse functions.
Step 4.3.4
Combine the opposite terms in .
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Step 4.3.4.1
Add and .
Step 4.3.4.2
Add and .
Step 4.4
Since and , then is the inverse of .