Precalculus Examples

Find the Inverse f(x)=2/(x-3)
Step 1
Write as an equation.
Step 2
Interchange the variables.
Step 3
Solve for .
Tap for more steps...
Step 3.1
Rewrite the equation as .
Step 3.2
Find the LCD of the terms in the equation.
Tap for more steps...
Step 3.2.1
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Step 3.2.2
Remove parentheses.
Step 3.2.3
The LCM of one and any expression is the expression.
Step 3.3
Multiply each term in by to eliminate the fractions.
Tap for more steps...
Step 3.3.1
Multiply each term in by .
Step 3.3.2
Simplify the left side.
Tap for more steps...
Step 3.3.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.3.2.1.1
Cancel the common factor.
Step 3.3.2.1.2
Rewrite the expression.
Step 3.3.3
Simplify the right side.
Tap for more steps...
Step 3.3.3.1
Apply the distributive property.
Step 3.3.3.2
Move to the left of .
Step 3.4
Solve the equation.
Tap for more steps...
Step 3.4.1
Rewrite the equation as .
Step 3.4.2
Add to both sides of the equation.
Step 3.4.3
Divide each term in by and simplify.
Tap for more steps...
Step 3.4.3.1
Divide each term in by .
Step 3.4.3.2
Simplify the left side.
Tap for more steps...
Step 3.4.3.2.1
Cancel the common factor of .
Tap for more steps...
Step 3.4.3.2.1.1
Cancel the common factor.
Step 3.4.3.2.1.2
Divide by .
Step 3.4.3.3
Simplify the right side.
Tap for more steps...
Step 3.4.3.3.1
Cancel the common factor of .
Tap for more steps...
Step 3.4.3.3.1.1
Cancel the common factor.
Step 3.4.3.3.1.2
Divide by .
Step 4
Replace with to show the final answer.
Step 5
Verify if is the inverse of .
Tap for more steps...
Step 5.1
To verify the inverse, check if and .
Step 5.2
Evaluate .
Tap for more steps...
Step 5.2.1
Set up the composite result function.
Step 5.2.2
Evaluate by substituting in the value of into .
Step 5.2.3
Simplify each term.
Tap for more steps...
Step 5.2.3.1
Multiply the numerator by the reciprocal of the denominator.
Step 5.2.3.2
Cancel the common factor of .
Tap for more steps...
Step 5.2.3.2.1
Cancel the common factor.
Step 5.2.3.2.2
Rewrite the expression.
Step 5.2.4
Combine the opposite terms in .
Tap for more steps...
Step 5.2.4.1
Add and .
Step 5.2.4.2
Add and .
Step 5.3
Evaluate .
Tap for more steps...
Step 5.3.1
Set up the composite result function.
Step 5.3.2
Evaluate by substituting in the value of into .
Step 5.3.3
Simplify the denominator.
Tap for more steps...
Step 5.3.3.1
Subtract from .
Step 5.3.3.2
Add and .
Step 5.3.4
Multiply the numerator by the reciprocal of the denominator.
Step 5.3.5
Cancel the common factor of .
Tap for more steps...
Step 5.3.5.1
Cancel the common factor.
Step 5.3.5.2
Rewrite the expression.
Step 5.4
Since and , then is the inverse of .