Trigonometry Examples

Find the Inverse y=e^(x-1)
Step 1
Interchange the variables.
Step 2
Solve for .
Tap for more steps...
Step 2.1
Rewrite the equation as .
Step 2.2
Take the natural logarithm of both sides of the equation to remove the variable from the exponent.
Step 2.3
Expand the left side.
Tap for more steps...
Step 2.3.1
Expand by moving outside the logarithm.
Step 2.3.2
The natural logarithm of is .
Step 2.3.3
Multiply by .
Step 2.4
Add to both sides of the equation.
Step 3
Replace with to show the final answer.
Step 4
Verify if is the inverse of .
Tap for more steps...
Step 4.1
To verify the inverse, check if and .
Step 4.2
Evaluate .
Tap for more steps...
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
Simplify each term.
Tap for more steps...
Step 4.2.3.1
Use logarithm rules to move out of the exponent.
Step 4.2.3.2
The natural logarithm of is .
Step 4.2.3.3
Multiply by .
Step 4.2.4
Combine the opposite terms in .
Tap for more steps...
Step 4.2.4.1
Add and .
Step 4.2.4.2
Add and .
Step 4.3
Evaluate .
Tap for more steps...
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
Combine the opposite terms in .
Tap for more steps...
Step 4.3.3.1
Subtract from .
Step 4.3.3.2
Add and .
Step 4.3.4
Exponentiation and log are inverse functions.
Step 4.4
Since and , then is the inverse of .