Find g(f(x)) f(x)=1/(x^2+23) , g(x) = square root of x+100

Math
,
Set up the composite result function.
Evaluate by substituting in the value of into .
To write as a fraction with a common denominator, multiply by .
Combine the numerators over the common denominator.
Reorder terms.
Rewrite in a factored form.
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Apply the distributive property.
Multiply by .
Add and .
Rewrite as .
Multiply by .
Combine and simplify the denominator.
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Multiply and .
Raise to the power of .
Raise to the power of .
Use the power rule to combine exponents.
Add and .
Rewrite as .
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Use to rewrite as .
Apply the power rule and multiply exponents, .
Combine and .
Cancel the common factor of .
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Cancel the common factor.
Divide by .
Simplify.
Combine using the product rule for radicals.
Find g(f(x)) f(x)=1/(x^2+23) , g(x) = square root of x+100

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