SOLUTION: 1. Determine the domain and range for f(x)=3+√(x-5). 2. Given that f(x)=3+√(x-5) and g(x)=tan x. determine fog(x).

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f(x) and y are the same thing. So write it as:



What's under the square root, x-5, cannot be negative so it must be
greater than or equal to 0, so we have:


}

So the domain is the set of all x-values greater than or equal to 5.

{x | x ≥ 5} or in interval notation: [5,)

Since the square root  is never negative we can write



We can add 3 to both sides to make the right side of f(x) above:



And since  





So the range is the set of all y-values greater than or equal to 3.

{y | y ≥ 3} or in interval notation: [3,).  
 
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f∘g(x) = , so we substitute the right side of
g(x) for x in the right side of f(x).

f∘g(x).

Edwin