Algebra Examples

Find the Domain (fog)(x) , f(x)=1/(x+3) , g(x)=2/x
, ,
Set up the composite result function.
Evaluate by substituting in the value of into .
Simplify the denominator.
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Multiply by .
Combine the numerators over the common denominator.
Multiply the numerator by the reciprocal of the denominator.
Multiply by .
Set the denominator in equal to to find where the expression is undefined.
Solve for .
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Subtract from both sides of the equation.
Divide each term by and simplify.
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Divide each term in by .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Move the negative in front of the fraction.
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
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