Trigonometry Examples

Find the Inverse g(x)=7+(3x)/4
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
Subtract from both sides of the equation.
Step 3.3
Multiply both sides of the equation by .
Step 3.4
Simplify both sides of the equation.
Tap for more steps...
Step 3.4.1
Simplify the left side.
Tap for more steps...
Step 3.4.1.1
Simplify .
Tap for more steps...
Step 3.4.1.1.1
Cancel the common factor of .
Tap for more steps...
Step 3.4.1.1.1.1
Cancel the common factor.
Step 3.4.1.1.1.2
Rewrite the expression.
Step 3.4.1.1.2
Cancel the common factor of .
Tap for more steps...
Step 3.4.1.1.2.1
Factor out of .
Step 3.4.1.1.2.2
Cancel the common factor.
Step 3.4.1.1.2.3
Rewrite the expression.
Step 3.4.2
Simplify the right side.
Tap for more steps...
Step 3.4.2.1
Simplify .
Tap for more steps...
Step 3.4.2.1.1
Apply the distributive property.
Step 3.4.2.1.2
Combine and .
Step 3.4.2.1.3
Multiply .
Tap for more steps...
Step 3.4.2.1.3.1
Combine and .
Step 3.4.2.1.3.2
Multiply by .
Step 3.4.2.1.4
Move the negative in front of the fraction.
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
Combine the numerators over the common denominator.
Step 5.2.4
Simplify each term.
Tap for more steps...
Step 5.2.4.1
Apply the distributive property.
Step 5.2.4.2
Multiply by .
Step 5.2.4.3
Cancel the common factor of .
Tap for more steps...
Step 5.2.4.3.1
Cancel the common factor.
Step 5.2.4.3.2
Rewrite the expression.
Step 5.2.5
Simplify terms.
Tap for more steps...
Step 5.2.5.1
Combine the opposite terms in .
Tap for more steps...
Step 5.2.5.1.1
Subtract from .
Step 5.2.5.1.2
Add and .
Step 5.2.5.2
Cancel the common factor of .
Tap for more steps...
Step 5.2.5.2.1
Cancel the common factor.
Step 5.2.5.2.2
Divide by .
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 each term.
Tap for more steps...
Step 5.3.3.1
Simplify the numerator.
Tap for more steps...
Step 5.3.3.1.1
Combine the numerators over the common denominator.
Step 5.3.3.1.2
Factor out of .
Tap for more steps...
Step 5.3.3.1.2.1
Factor out of .
Step 5.3.3.1.2.2
Factor out of .
Step 5.3.3.1.2.3
Factor out of .
Step 5.3.3.2
Combine and .
Step 5.3.3.3
Multiply by .
Step 5.3.3.4
Reduce the expression by cancelling the common factors.
Tap for more steps...
Step 5.3.3.4.1
Reduce the expression by cancelling the common factors.
Tap for more steps...
Step 5.3.3.4.1.1
Factor out of .
Step 5.3.3.4.1.2
Factor out of .
Step 5.3.3.4.1.3
Cancel the common factor.
Step 5.3.3.4.1.4
Rewrite the expression.
Step 5.3.3.4.2
Divide by .
Step 5.3.3.5
Cancel the common factor of .
Tap for more steps...
Step 5.3.3.5.1
Cancel the common factor.
Step 5.3.3.5.2
Divide by .
Step 5.3.4
Combine the opposite terms in .
Tap for more steps...
Step 5.3.4.1
Subtract from .
Step 5.3.4.2
Add and .
Step 5.4
Since and , then is the inverse of .