# Find the Domain f(x)=(4x^2)/(3x)+4 , g(x)=9/x , g(f(x))

, ,
Set up the composite result function.
Evaluate by substituting in the value of into .
Set the denominator in equal to to find where the expression is undefined.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Set the denominator in equal to to find where the expression is undefined.
Solve for .
Reduce the expression by cancelling the common factors.
Factor out of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Find the LCD of the terms in the equation.
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
Since contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part then find LCM for the variable part .
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
Since has no factors besides and .
is a prime number
The number is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of is the result of multiplying all prime factors the greatest number of times they occur in either number.
Multiply each term by and simplify.
Multiply each term in by in order to remove all the denominators from the equation.
Simplify each term.
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Multiply by .
Multiply by .
Solve the equation.
Subtract from both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Find the Domain f(x)=(4x^2)/(3x)+4 , g(x)=9/x , g(f(x))
Scroll to top