Algebra Examples

Find the Domain of the Composition f(g(x)) f(x)=2/(x-7) , g(x) = square root of x-2
,
Step 1
Set up the composite result function.
Step 2
Evaluate by substituting in the value of into .
Step 3
Set the radicand in greater than or equal to to find where the expression is defined.
Step 4
Add to both sides of the inequality.
Step 5
Set the denominator in equal to to find where the expression is undefined.
Step 6
Solve for .
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Step 6.1
Add to both sides of the equation.
Step 6.2
To remove the radical on the left side of the equation, square both sides of the equation.
Step 6.3
Simplify each side of the equation.
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Step 6.3.1
Use to rewrite as .
Step 6.3.2
Simplify the left side.
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Step 6.3.2.1
Simplify .
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Step 6.3.2.1.1
Multiply the exponents in .
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Step 6.3.2.1.1.1
Apply the power rule and multiply exponents, .
Step 6.3.2.1.1.2
Cancel the common factor of .
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Step 6.3.2.1.1.2.1
Cancel the common factor.
Step 6.3.2.1.1.2.2
Rewrite the expression.
Step 6.3.2.1.2
Simplify.
Step 6.3.3
Simplify the right side.
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Step 6.3.3.1
Raise to the power of .
Step 6.4
Move all terms not containing to the right side of the equation.
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Step 6.4.1
Add to both sides of the equation.
Step 6.4.2
Add and .
Step 7
The domain is all values of that make the expression defined.
Interval Notation:
Set-Builder Notation:
Step 8